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Difficulty:
25%
(medium)
Question Stats:
89% (02:46) correct
11%
(02:37)
wrong
based on 79
sessions
History
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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
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Bunuel
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.
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General Discussion
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.
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.
Bunuel
Bunuel
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
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
_________________
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
_________________
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