jsasipriya 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 return trip 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
OA E
Can someone help me?
Thanks!
Since on the first day each bus travels for 2 hours, the total time to cover the distance between the two cities is 2+2 = 4 hours.
On the return trip, one bus leaves 36 minutes earlier and the other bus leaves 24 minutes later. Thus, the earlier bus will travel 36+24 = 60 minutes = 1 hour longer than than the later bus. Since the total travel time to cover the distance must remain 4 hours, the earlier bus will travel for 2.5 hours and the later bus will travel for 1.5 hours.
Since the earlier bus travels for 2 hours on the first day and 2.5 hours on the return trip, the earlier bus travels for 1/2 hour more on the return trip. Since the meeting point on the return trip is 24 miles from the meeting point on the first day, during its 1/2 hour of extra travel time the earlier bus has to travel 24 more miles than it did on the first day.
Now we can plug in the answer choices, which represent the distance between the 2 cities. On the first day, the earlier bus will travel 1/2 the distance, since the two buses are traveling toward each other at the same rate. On the return trip, the earlier bus must travel 24 more miles during its 1/2 hour of extra travel time.
Answer choice C: 96 miles between the 2 cities
Distance traveled by the earlier bus on the first day = 1/2*96 = 48 miles.
Rate of the earlier bus = d/t = 48/2 = 24 miles per hour.
On the return trip, the earlier bus will travel r*t = 24*(1/2) = 12 more miles.
The distance needs to be doubled. Since 2*96 = 192, the correct answer is
E.
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