Test: Distance And Speed- 1 - GMAT MCQ

Average speed :-

Total distance / Total time

⇒ (50+60) miles / (2+3) hours

⇒ 110/ 5  

⇒ 22 miles / hour

2xaxb
  a+b
2x60x80
  60+80
2x6x80
    14
480
  7
so (b) option

Solution:

- Alan's Journey:
- Alan started at 10.00am and reached Point B at 11.00am, so the total time taken by Alan = 1 hour.
- Alan's average speed = 30 miles per hour.
- Therefore, the distance between Point A and Point B = 30 miles (as distance = speed * time).

- Bob's Journey:
- Bob started 15 minutes (or 0.25 hours) after Alan started his journey.
- Bob travels the same route as Alan, so the distance between Point A and Point B is the same for Bob.
- Bob reaches Point B at the same time as Alan, so Bob takes 45 minutes (or 0.75 hours) to cover the distance.
- Let Bob's average speed be x miles per hour, then the distance between Point A and Point B = x * 0.75.

- Equating the distances:
- As the distance between Point A and Point B is the same for both Alan and Bob:
- 30 = x * 0.75
- x = 30 / 0.75
- x = 40 miles per hour.

Therefore, Bob's average speed is 40 miles per hour, which matches option E.

Solution:

• Let the speed of the boat in still water be x mph and the speed of the current be 1 mph.
• When the boat travels downstream with the current, the effective speed is (x + 1) mph. The time taken to reach the destination is 2.5 hours.
• When the boat travels upstream against the current, the effective speed is (x - 1) mph. The time taken to cover the same distance is 3.5 hours.

We can use the formula: Distance = Speed * Time

• Distance downstream = (x + 1) * 2.5 = 2.5x + 2.5
• Distance upstream = (x - 1) * 3.5 = 3.5x - 3.5
• Since the distances covered in both directions are the same, we can equate the two expressions:
  2.5x + 2.5 = 3.5x - 3.5

Solving for x:
2.5 + 3.5 = 3.5x - 2.5x
6 = 1.0x
x = 6
Therefore, the speed of the boat in still water is 6 mph, which corresponds to option D.

Solution:

Statement 1: It took a total of 5 hours to complete the entire distance.

- Let the total distance be D miles.
- Let the time taken to cover the first part be 2x hours and the time taken to cover the remaining part be 3x hours.
- Using the formula Distance = Speed x Time, we can write the equations:
- Distance covered in the first part = 30 * 2x = 60x
- Distance covered in the remaining part = 50 * 3x = 150x
- Total distance = 60x + 150x = 210x

- We are given that the total time taken is 5 hours, so:
- 2x + 3x = 5
- 5x = 5
- x = 1

- Therefore, the total distance D = 210x = 210 * 1 = 210 miles.

Statement 2: 2/7th of the entire distance was covered during the first part.

- Let the total distance be D miles.
- According to the statement, the distance covered in the first part = 2/7 * D
- Therefore, the distance covered in the remaining part = D - 2/7 * D = 5/7 * D

- However, this information alone does not provide us with enough information to determine the total distance that Charles travelled.

Conclusion: Statement (1) alone is sufficient to answer the question, but statement (2) alone is not sufficient. Therefore, the correct answer is A.

Step 1: Question statement and Inferences

Let the two dogs meet at a distance of x miles from the Starting position of Dog 1.

So, Dog 1 covers a distance of x miles at a speed of 12 mph to reach the meeting point.

In the same time, Dog 2 covers a distance of (2-x) miles at a speed of 8 mph to reach the meeting point

Step 2: Finding required values

We know that

Since the time taken by Dog 1 to reach the meeting point is equal to the time taken by Dog 2 to reach the meeting point, we can write:

The dogs will meet 6/5 miles from Dog 1’s starting position.

Answer: Option (B)

Step 1: Question statement and Inferences

Riding 10 miles at her new speed took Sam 10 minutes less than riding the same distance at 12 miles per hour. What was this new speed?

Step 2: Finding required values

Start by finding the time it took Sam to reach the top of the hill.

Her uphill speed, u = 12 miles per hour

Distance travelled = 10 miles

Now considering the downhill journey,

Step 3: Calculating the final answer

Answer: Option (B)

Step 1: Question statement and Inferences

Johnny drove three segments for h hours each. His speeds were m, m + s, and 2m. The question asks for the representation of the distance which he drove. 

We know that

Step 2: Finding required values

Multiply the time driven, h for each segment, by the speed driven for that segment, to get distances. These are hm, h(m + s), and 2hm, respectively.

Step 3: Calculating the final answer

The total distance traveled is hm + h(m + s) + 2hm, which factors out to h(4m +s). 

Answer: Option (B)

Given:

Let’s call Emily’s journey from her home till she meets her friend as her “Forward Journey” and her journey from when she meets her friend  till her home as her “Return Journey”

Forward Journey

• Home to “Ran out of fuel” point
  • Distance travelled = x miles
  • Driving speed = p miles per hour
  • Let the time taken be t₁ hours.
• “Ran out of fuel” point till she meets her friend
  • Speed of walking= 8 meters per minute
  • Let the distance covered be y miles
  • Let the time taken while walking = t₂ hours.
• Total distance covered in Forward Journey = (x + y) miles

Return Journey

• From when Emily meets her friend to Home
  • Total distance travelled = (x + y) miles
    • Distance in forward journey = Distance covered in return journey
  • Speed of driving = 50% more than p miles per hour
  • Let the total time taken for the return journey be t₃ hours.

So our DST table would look like this:

*(t₁ + t₂ + t₃) = t hours

To Find: How many miles she has walked her motorcycle = y = ?

Linkages

1. To find the value of y, let’s focus on the Home to “Ran out of fuel” point row of the DST table.
   1. To calculate the value of y from here, we need to know the speed and the time, but t₂ is unknown to us.
2. We observe that t₂ is also present in the equation of time (t₁ + t₂ + t₃) = t hours
   1. To calculate t₂ we need the value of t₁ and t₃.
3. We observe that t₃ is present in the “Emily meets her friend to home row” of the DST table.
   1. From here we can express t₃ in terms of x, y and p.
4. We observe that t₁ is present in the Home to “Ran out of fuel” point row of the DST table.
   1. From here we can express t₁ in terms of x and p.
5. So we will have 4 equations and 4 variables, and thus we will be able to find the value of y.

Approach

1. From the “Emily meets her friend to home” row of the DST table, we will get t3

•  in terms of x , y and p.
• From home to “Ran out of fuel” point row of the DST table, we will get t1
•  in terms of x and p.
• From “Ran out of fuel point to Emily meets her friend” row of the DST table, we will get t2
•  in terms of y.
• Putting values of t₁, t₂ and t₃ in the equation (t₁ + t₂ + t₃) = t hours, we will be able to find the value of unknown i.e. p.

Calculation

1. From the “Emily meets her friend to home” row of the DST table, we will get t₃  in terms of x , y and p.

2. From home to “Ran out of fuel” point row of the DST table, we will get t1 in terms of x and p.

3. From “Emily “meets her friend” to home  row of the DST table, we will get t2 in terms of y.

1. Speed = 8 meters per minute
   1. Here speed is given to us in different units
   2. Making the units consistent
   3. Speed =

4. (t₁ + t₂ + t₃) = t hours

1. Putting values of t₁, t₂ and t_3, we have

• To get rid of  the variable 'p' in the denominator multiply both sides of the equation with 'p'
• So, we get :

To get rid of the decimal in the denominator multiply both sides of the equation by 1/10

• LCM (15,10, 3) = 30
• Multiplying both sides of the equation by 30, we get :

Correct Answer: Option D

In GMAT questions like this one, relying solely on an algebraic approach can slow you down. The most efficient method to solve this within 2 minutes is to use simple values for the unknowns.

Let's assume x=100x = 100x=100 miles and y=10y = 10y=10 miles per hour. This means Karen takes 10 hours to travel from her home to her office.

For her return trip, she travels 10 miles at the same speed, taking 1 hour. After stopping for an hour, she has 8 hours left to travel the remaining 90 miles (since the total travel time needs to match the 10 hours taken to reach the office). Therefore, she must travel the remaining 90 miles at an average speed of 90/8= 11.25 miles per hour.

Comparing this new speed to her original speed of 10 miles per hour, the percentage increase in speed is 
(11.25−10​)/10 * 100 =12.5%
 Now, we need to find the option that matches this percentage increase.

Looking at the options, we notice that the denominator is either x−y−10 or y−x−10. Since y is less than x, y−x−10 would be negative. Since we need a percentage increase (a positive value), we can eliminate options with y−x−10 as the denominator. Thus, options C, D, and E are eliminated, leaving us with A and B.

Option A has a much larger numerator, making it an unlikely percentage increase. Substituting x=100 and y=10 into option B:

100y/ (x-y-10) = 100 *10 /100-10-10 = 1000/80 =12.5 

This matches our required percentage increase, allowing us to rule out option A. Therefore, the correct answer is B.

Explanation:
A to B

• Speed = 1.2 min/km (note that the speed is not in usual distance/time format)
• Time = 3hrs to 5hrs = 180mins to 300mins
• Therefore, Distance =Time/Speed =180/1.2 to 300/1.2=150km to 250km

B to A

• Speed = 1 min/km (note that the speed is not in usual distance/time format)
• Time = 2hrs to 3hrs = 120mins to 180mins
• Therefore, Distance =Time/Speed =120/1to180/1=120km to 180km
  
  Based on both the above ranges, the only possible distance, among the options, is 160km

Solution:

Given:
- Phil drives east from his home for 2 hours before realizing he will run out of fuel in another 70 miles.
- He drives for another 10 miles east before returning back home via the same route.
- Phil returns home with fuel left for another 10 miles.

To find:
- The total time Phil takes for his journey eastwards.

Explanation:
- When Phil realizes he will run out of fuel in 70 miles, he has already driven for 2 hours.
- This means that he can drive for another 70 miles in 2 hours.
- After driving another 10 miles east, he returns home with fuel left for another 10 miles.
- Therefore, the total distance Phil covered in one direction is 70 + 10 = 80 miles.
- Since Phil drives at a constant speed throughout his journey, we can assume that his speed is constant.
- Time = Distance / Speed
- Time taken to cover 80 miles = 2 hours
- Therefore, the time Phil takes for his journey eastwards is 2 hours to drive 80 miles.

Conclusion:
- Phil takes 2.5 hours for his journey eastwards. (Option B)

Let’s let m = the time, in minutes, that it takes Tom to walk s feet at a rate of x ft/min. Thus, we have the following distance equation for Tom’s usual day:
x * m = s
m = s/x
Tom’s rate today - x meters/min - is equivalent to x/0.3 ft/min, and we use this value in his distance equation for today. Letting n = the time, in minutes, that it takes him to walk 10% more distance than normal (1.1s feet) at a rate of x/0.3 ft/min, we have today’s equation as:
x/0.3 * n = 1.1s
n = 1.1s / (x/0.3)
n = 0.33s/x
To determine the percent change in the time it takes him today, compared to his usual time, we use the percent change formula (New - Old)/Old * 100:
(0.33s/x - s/x) / (s/x) *100
(0.33s - s)/s *100
(0.33 - 1)/1 *100 = - 67 percent
Thus, today, Tom took 67% less time than on a usual day.

Analysis:

- From the question, we know that the train takes 2 hours to travel from one station to the other.
- We need to find the distance between the two stations.

Statement 1:
- The train covers one third of the total distance in the first hour at an average speed of 80 mph.
- Since the train covers one third of the total distance in the first hour, it covers the remaining two thirds of the distance in the second hour.
- Therefore, using the information from statement 1 alone, we can calculate the total distance.
- This statement alone is sufficient to answer the question.

Statement 2:
- The average speed during the second hour is 160 mph.
- This statement alone does not provide information on the distance or the time taken in the first hour.
- Therefore, statement 2 alone is not sufficient to answer the question.

Conclusion:
- Statement 1 alone is sufficient to answer the question.
- The correct answer is option A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Correct Answer :- e

Explanation : Speed downstream = (5 + 1) kmph = 6 mph.

Speed upstream = (5 - 1) kmph = 4 mph.

Let the required distance be x m.

Then,   x/6 + x/4 = 1

 2x + 3x = 12

 5x = 12

 x = 2.4 

Therefore, the total distance covered is 2 * 2.4 = 4.8 miles.