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Test: Distance/Rate Problems - GMAT MCQ


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10 Questions MCQ Test - Test: Distance/Rate Problems

Test: Distance/Rate Problems for GMAT 2025 is part of GMAT preparation. The Test: Distance/Rate Problems questions and answers have been prepared according to the GMAT exam syllabus.The Test: Distance/Rate Problems MCQs are made for GMAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Distance/Rate Problems below.
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Test: Distance/Rate Problems - Question 1
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Aaron travels from town X to town Y and then back from town Y to town X, taking different routes in each direction. If his speed when travelling from town X to town Y is 36 miles per hour, and his speed when travelling in the opposite direction is 48 miles per hour, what is his average speed for the entire journey?

1) The length of the return trip is 24% of the entire distance travelled.
2) The length of the return trip is 100 miles.

Detailed Solution for Test: Distance/Rate Problems - Question 1

Statement (1) indicates that the length of the return trip is 24% of the entire distance travelled.

Statement (2) provides that the return trip distance is 100 miles.

Using both statements together, we can deduce the entire distance travelled as follows:

  • If the return trip is 24% of the total distance, then the total distance is 100 miles / 0.24, which equals approximately 416.67 miles.
  • Therefore, the one-way distance from town X to town Y is 316.67 miles (416.67 - 100).
  • Using the speeds provided, we can find the total time for the journey: the time from X to Y is 316.67 miles / 36 mph, and the time from Y to X is 100 miles / 48 mph.
  • The average speed is the total distance divided by the total time.
  • By calculating these, we find that both statements together provide sufficient information to determine the average speed for the entire journey.
  • Therefore, the correct answer is (E): BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
Test: Distance/Rate Problems - Question 2
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Amy reached from her home to her aunt’s place in 75 minutes. What is the average speed at which Amy drove her car?

(1) She travelled the first 30 minutes at 60 miles per hour and remaining at 80 miles per hour.
(2) The total distance between Amy and her aunt’s home is 90 miles.

Detailed Solution for Test: Distance/Rate Problems - Question 2

Let's examine each statement separately to see if it provides the necessary information:

Statement (1):

  • Amy travelled the first 30 minutes at 60 miles per hour and the remaining time (75 - 30 = 45 minutes) at 80 miles per hour.

Using this information, we can calculate the distance for each segment of the trip:

  1. Distance for the first 30 minutes: Since speed = 60 mph, in 30 minutes (or 0.5 hours), she travelled: Distance=60×0.5=30 miles
  2. Distance for the remaining 45 minutes: Since speed = 80 mph, in 45 minutes (or 0.75 hours), she travelled: Distance2=80×0.75=60 miles

The total distance travelled is:

Total Distance=30+60=90 miles

Now, we can calculate the average speed:

Average Speed=Total Distance /Total Time

= 90 miles/1.25 hours = 72 miles per hour

Thus, Statement (1) alone is sufficient to determine the average speed.

Statement (2):

  • The total distance between Amy and her aunt’s home is 90 miles.

Given that the total distance is 90 miles and the total time taken is 75 minutes (or 1.25 hours), we can calculate the average speed:

Average Speed=Total Distance/Total Time

=90 miles/1.25 hours = 72 miles per hour

Thus, Statement (2) alone is also sufficient to determine the average speed.

Conclusion

Both statements independently provide enough information to answer the question.

The correct answer is (c) EACH statement ALONE is sufficient to answer the question asked.

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Test: Distance/Rate Problems - Question 3
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A ferry crosses a lake and then returns to its starting point by the same route. The first time it crosses the lake, the ferry travels at 15 kilometers per hour. The ferry’s return trip takes 3 hours. How many hours does the ferry take for the first leg of the trip?

(1) The ferry’s average speed for the entire round trip is 12 kilometers per hour.
(2) The distance the ferry covers to cross the lake once is 30 kilometers.

Test: Distance/Rate Problems - Question 4
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In an endurance race, a car drove the whole race at a constant speed of 3 miles per minute to cover the total race distance D. Was the value of D greater than 500 miles?

Statement 1. The time taken by the car to cover D was more than 2 hours.
Statement 2. The time taken by the car to cover D was less than 2.75 hours.
Detailed Solution for Test: Distance/Rate Problems - Question 4

Given:
In this question, we are given

  • In an endurance race, a car drove the whole race at a constant speed of 3 miles per minute to cover the total race distance D.

To find:
We need to determine

  • Whether the value of D greater than 500 miles or not.

Approach and Working:

  • Speed of the car = 3 miles per minute = (3 x 60) miles per hour = 180 miles per hour

As we already know the constant speed of the car is 180 miles per hour, to determine whether D was more than 500 miles or not, we need to know the time duration for which the car was driven.

Analysing Statement 1
As per the information given in statement 1, the car took more than 2 hours to complete the race.
From this statement, we can say that

  • The car drove more than (180 x 2) = 360 miles in the race.
     However, we cannot say whether the distance the car was driven was more than 500 miles or not.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, the car took less than 2.75 hours to complete the race.
From this statement, we can say that

  • The car drove less than (180 x 2.75) = 495 miles in the race.
    Therefore, we can definitely say that the distance the car was driven was not more than 500 miles.

Hence, statement 2 is sufficient to answer the question.
Hence, the correct answer is option B.

Test: Distance/Rate Problems - Question 5
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Bob ran a 20-mile race. At what time did he finish the race?

1. He started the race at 8:05 am and his average speed for the first 10 miles of the race was 8 miles per hour.
2. He ran at a constant rate and had completed half of the amount of running time at 9:20 AM and had completed 80% of the running time at 10:05 AM.
Detailed Solution for Test: Distance/Rate Problems - Question 5

Given:

  • Bob ran a 20-mile race.

To find:

  • The time at which he finished the race.

Analysing Statement 1
As per the information given in statement 1, Bob started the race at 8:05 am and his average speed for the first 10 miles of the race was 8 miles per hour.

  • However, we don’t have any information about Bob’s average speed for the last 10 miles.

Hence, statement 1 is not sufficient to answer the question.
Analysing Statement 2
As per the information given in statement 2, Bob ran at a constant rate and had completed half of the amount of running time at 9:20 AM and had completed 80% of the running time at 10:05 AM.

  • So, he completed 30% of the distance in 45 minutes.

As he was running at a constant rate, we can say that

  • He completed 50% distance in 75 minutes = 1 hour 15 minutes
    And he completed 100% distance in 150 minutes = 2 hours 30 minutes

Therefore, Bob’s starting time = (9: 20 am – 1hour 15 minutes) = 8: 05 am
And Bob’s finishing time = (8: 05 am + 2 hours 30 minutes) = 10: 35 am

Hence, statement 2 is sufficient to answer the question.
Hence, the correct answer is option B.

Test: Distance/Rate Problems - Question 6
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Today, Samson’s Train traveled at a constant rate along a straight North-South route that included the famous 10-mile long Chasm Bridge. Was Samson’s Train on the Chasm Bridge at 2:00 p.m.?

(1) At 9:00 a.m., Samson’s Train was 200 miles north of the Chasm Bridge, and at 4:00 p.m, the train was 140 miles south of Chasm Bridge.
(2) Samson’s Train started its trip at 6:00 a.m., and traveled at a rate of less than 70 miles per hour.
Detailed Solution for Test: Distance/Rate Problems - Question 6

Statement (1) alone: sufficient

  • At 9:00 a.m.: 200 miles north of the bridge.

  • At 4:00 p.m.: 140 miles south of the bridge.

  • In 7 hours it moved 200 + 140 = 340 miles ⇒ constant speed = 340/7 ≈ 48.57 mph.

  • Time from 9:00 a.m. to reach the bridge’s near end: 200 / 48.57 ≈ 4.12 hours ⇒ about 1:07 p.m.

  • Time to cross the 10-mile bridge at that speed: 10 / 48.57 ≈ 0.21 hours ≈ 12.3 minutes.
    So it leaves the bridge around 1:19 p.m.

  • At 2:00 p.m. it is already past the bridge. So the answer (No) is determined.
    → Sufficient.

Statement (2) alone: not sufficient

  • Start time and speed < 70 mph do not tell where the train is at 2:00 p.m. relative to the bridge.
    → Insufficient.

Therefore, Statement (1) alone is sufficient; Statement (2) alone is not.

Test: Distance/Rate Problems - Question 7
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Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive?

(1) Al drove for 3/4 as much time as Barb did.
(2) Al's average driving speed for the entire trip was 4/5 of Barb's average driving speed for the trip.
Test: Distance/Rate Problems - Question 8
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On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?

(1) 2x + 3y = 280
(2) y = x + 10
Detailed Solution for Test: Distance/Rate Problems - Question 8

Average speed = Total distance/Total time ;
Total distance = Avg speed * Total time

Marta averaged x miles per hour for 2 hours = 2x
y miles per hour for the remaining 3 hours = 3y
Total distance = 2x+3y

Total time = 2+3 = 5 hrs

Avg speed = 2x+3y/5

Statement 1: 2x+3y=280

Avg speed = 280/5 = 56m/h. Sufficient.

Statement 2: y = x + 10, Not sufficient.

Test: Distance/Rate Problems - Question 9
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Tom and Samuel are riding motorcycles down the highway at constant speeds. If Tom is now 2 miles ahead of Samuel, How many minutes from now (i.e., after now) until Tom is 3 miles ahead?”

(1) Tom is traveling at 70 miles per hour and Samuel is traveling at 60 miles per hour.
(2) Tom left 5 minutes before Samuel.
Detailed Solution for Test: Distance/Rate Problems - Question 9

Statement One Alone:
⇒Tom is traveling at 70 miles per hour and Samuel is traveling at 60 miles per hour.
Thus, the distance between Tom and Samuel is increasing at a rate of 70 - 60 = 10 miles per hour. If the distance increases by 10 miles each hour, then the distance between the two drivers will increase by 1 mile in 1/10 × 60 minutes = 6 minutes. So, Tom will be 3 miles ahead of Samuel in 6 minutes. Statement one is sufficient.
Eliminate answer choices B, C, and E.

Statement Two Alone:
⇒ Tom left 5 minutes before Samuel.
Without knowing anything about the speeds of each driver or the difference between the speeds of the two drivers, we cannot determine the number of minutes for Tom to increase the distance to 3 miles. For instance, if Tom travels at 70 mph and Samuel travels at 60 mph, then Tom will be 3 miles ahead of Samuel in 6 minutes, as we calculated earlier. On the other hand, if Tom travels at 80 mph and Samuel travels at 60 mph, then the distance between the two drivers will increase by 80 - 60 = 20 miles per hour. Thus, Tom will be 3 miles ahead of Samuel in 1/20 × 60 minutes = 3 minutes. Since there is more than one possible answer to the question, statement two alone is not sufficient.

Test: Distance/Rate Problems - Question 10
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A cyclist rides to the top of a hill and then coasts back down by the same route. The entire trip takes 4 hours. What is his average (arithmetic mean) speed when climbing the hill?

(1) The cyclist's average speed over the entire trip was 6 miles per hour.
(2) The distance to the top of the hill was 12 miles, and the cyclist's average speed on the downward trip was 18 miles per hour.
Detailed Solution for Test: Distance/Rate Problems - Question 10

Statement 1 gives the information about the total distance. But there is no clue of the speed climbing the hill. Not sufficient

Statement 2 - Distance for downtrip will also be 12. We can find the time taken for covering downtrip which is 12/18 or 2/3 hr.
Time taken for uphill = 4-2/3
= 10/3
Distance = 12

Avg speed can be found out. Sufficient

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