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Difficulty:
45%
(medium)
Question Stats:
72% (02:32) correct
28%
(03:06)
wrong
based on 373
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Two motorists start a journey at opposite ends of the state and travel the same road toward one another. Motorist A travels the 375 miles across the state in 5 hours, while Motorist B travels at an average rate one-third slower than Motorist A travels. If each motorist finishes where the other started and both drove continuously until each of the respective trips was completed, how far had Motorist A driven, in miles, when his car passed that of Motorist B?
A. 275
B. 250
C. 225
D. 215
E. 210
A. 275
B. 250
C. 225
D. 215
E. 210
05 May 2017, 04:09
Kudos
Bookmarks
I think Bunuel "Motorist B travels at an average rate one-third slower than Motorist B travels" should be replaced with "Motorist B travels at an average rate one-third slower than Motorist A travels". With that assumption:
Speed of A = 375/5 = 75 miles per hour
Speed of B = 1/3 slower than A = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour
Since they are moving in opposite directions, their relative speed = (75+50) = 125 miles per hour.
Thus, time taken for the two motorists to meet = (relative distance)/(relative speed) = 375/125 = 3 hours
(here relative distance will be taken as complete distance 375 miles - because when they meet together both of them would have covered 375 miles in total)
In 3 hours, A would have covered = 3*75 = 225 miles. Thus C
Alternate:
IF speed of B is 1/3 slower than A, it means speed of B is 2/3 of A. This means ratio of Speed of A:Speed of B = 3:2
Both of them are starting at the same time and when they meet, each of them would have taken the same time to reach that point (obviously). So in the same time, the distances covered are always in the ratio of speeds. So the ratio of distance covered by A: distance covered by B = 3:2
And so when they meet and cover 375 miles in total (distance of A + distance of B equals the length of the road). To find their individual distances covered, we can just divide 375 in the ratio 3:2
Thus distance covered by A = 3/(3+2) * 375 = 225 miles. Thus C
Speed of A = 375/5 = 75 miles per hour
Speed of B = 1/3 slower than A = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour
Since they are moving in opposite directions, their relative speed = (75+50) = 125 miles per hour.
Thus, time taken for the two motorists to meet = (relative distance)/(relative speed) = 375/125 = 3 hours
(here relative distance will be taken as complete distance 375 miles - because when they meet together both of them would have covered 375 miles in total)
In 3 hours, A would have covered = 3*75 = 225 miles. Thus C
Alternate:
IF speed of B is 1/3 slower than A, it means speed of B is 2/3 of A. This means ratio of Speed of A:Speed of B = 3:2
Both of them are starting at the same time and when they meet, each of them would have taken the same time to reach that point (obviously). So in the same time, the distances covered are always in the ratio of speeds. So the ratio of distance covered by A: distance covered by B = 3:2
And so when they meet and cover 375 miles in total (distance of A + distance of B equals the length of the road). To find their individual distances covered, we can just divide 375 in the ratio 3:2
Thus distance covered by A = 3/(3+2) * 375 = 225 miles. Thus C
07 May 2017, 10:45
Kudos
Bookmarks
Speed of A = 375/5 = 75 miles per hour
Speed of B = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour
Since they are moving in opposite directions, their relative speed = (75+50) = 125 miles per hour.
time taken to cover the distance = 375/125 = 3 hrs
In 3 hours, A covered = 3*75 = 225 miles.
ANS C
Speed of B = 2/3 of the speed of A = 2/3 * 75 = 50 miles per hour
Since they are moving in opposite directions, their relative speed = (75+50) = 125 miles per hour.
time taken to cover the distance = 375/125 = 3 hrs
In 3 hours, A covered = 3*75 = 225 miles.
ANS C
