Test: Distance/Rate Problems - GMAT MCQ

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.

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.

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.

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.

Statement (1) provides information about the position of Samson's Train at two different times: 9:00 a.m. and 4:00 p.m. We know that at 9:00 a.m., the train was 200 miles north of the Chasm Bridge, and at 4:00 p.m., it was 140 miles south of the bridge. However, we don't have any information about the speed of the train or its direction. Therefore, statement (1) alone is not sufficient to determine if the train was on the Chasm Bridge at 2:00 p.m.

Statement (2) gives the starting time of the trip and mentions that the train traveled at a rate of less than 70 miles per hour. However, there is no information about the position of the train at any specific time or its direction of travel. Therefore, statement (2) alone is not sufficient to determine if the train was on the Chasm Bridge at 2:00 p.m.

When we combine the information from both statements, we still don't have any additional details about the position of the train at 2:00 p.m. Therefore, statements (1) and (2) together are not sufficient to answer the question.

In conclusion, the answer is (E): Statements (1) and (2) together are not sufficient to answer the question asked, and additional data are needed.

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.

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.

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