John and Clara set out from the same point at the same time and travel

Question

John and Clara set out from the same point at the same time and travel to the same destination. Clara travels at 5/8 of John’s speed and arrives 2 hours 30 minutes after John. How long does John take to complete the journey?

A. 3 hours 50 minutes
B. 4 hours 20 minutes
C. 4 hours
D. 4 hours 10 minutes
E. 4 hours 30 minutes

A. 3 hours 50 minutes
B. 4 hours 20 minutes
C. 4 hours
D. 4 hours 10 minutes
E. 4 hours 30 minutes

M47-37

Bunuel · Accepted Answer

GMAT Club Official Solution:

Let John’s time be t hours. Since Clara’s speed is 5/8 of John’s, her time is t/(5/8) = 8/5 * t.

8/5 * t = t + 2.5

3/5 * t = 2.5

t = 2.5 * 5/3 = 25/6 hours = 4 hours 10 minutes

Answer: D.

dp1234 · Answer

Since distance is same for both we can write Speed_Clara/Speed_John = Time_john/Time_clara. Let t be time for John, then we can write from question:

5/8 = t/(t+150) ..... converted time to min to avoid careless mistake (for me)
Solving this equation , t=250 min or  4hrs 10 min.

Dereno · Answer

Speed of Clara. = (5/8)* Speed of John.

Ratio of speed of Clara : John = 5:8

Then, the time ratio of Clara : John = 8x : 5x

Difference between the time

= 8x - 5x

= 3x = 150 minutes. (Or 2 hrs 30 minutes)

Thus, x = 50.

So time taken by John = 5x = 5*50 = 250 minutes =  4 hrs and 10 minutes.

Option D

egmat · Answer

When distance is the same,  Speed and Time are inversely proportional .

If Clara travels at  5/8  of John's speed, she takes  8/5  of John's time (the reciprocal!).

Solution: 
Let John's time =  T  hours

Since Clara's speed is  5/8  of John's speed:
→ Clara's time =  (8/5) × T

The difference in their times is  2 hours 30 minutes = 2.5 hours :

(8/5)T - T = 2.5 
 (8T - 5T)/5 = 2.5 
 3T/5 = 2.5 
 T = 2.5 × (5/3) 
 T = 12.5/3 = 25/6 hours

Converting to hours and minutes:
 25/6 hours = 4 hours + 1/6 hour = 4 hours 10 minutes

John and Clara set out from the same point at the same time and travel

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