rahulvsd wrote:A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the same trip again at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?
A. 48
B. 72
C. 96
D. 120
E. 192
We can plug in the answers, which represent the distance.
On the first day, since each bus travels for 2 hours at the same speed, point P -- the point where the two buses meet -- is 1/2 of the distance.
Since each bus travels 1/2 the distance in 2 hours, the total time needed to cover the entire distance = 4 hours.
On the second day, one bus leaves 1 hour earlier than the other.
Thus, the earlier bus travels 1/4 of the distance on its own.
Then the two buses work together to travel the remaining distance, with each bus traveling 1/2 the remaining distance.
When the correct answer is plugged in, the two buses must meet at a point 24 miles from point P.
Thus, the difference between point P and the distance traveled by the delayed bus must be 24 miles.
Answer choice C: 96 miles
Point P = (1/2)96 = 48 miles.
On the second day, the distance traveled by the earlier bus in the first hour = (1/4)96 = 24.
Remaining distance = 96-24 = 72.
Distance traveled by the delayed bus = (1/2)72 = 36.
Difference between Point P and the distance traveled by the delayed bus = 48-36 = 12.
Since the difference is supposed to be 24 miles -- twice as long -- the correct answer must be double answer choice C.
The correct answer is
E.
Answer choice E: 192 miles
Point P = (1/2)192 = 96 miles.
On the second day, the distance traveled by the earlier bus in the first hour = (1/4)192 = 48.
Remaining distance = 192-48 = 144.
Distance traveled by the delayed bus = (1/2)144 = 72.
Difference between Point P and the distance traveled by the delayed bus = 96-72 = 24.
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