Cities M and N are 600 miles apart. Bus A starts from city M towards N

Question

Cities M and N are 600 miles apart. Bus A starts from city M towards N at 9 AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40 miles per hour, the second one-third at 50 miles per hour and the third one-third at 60 miles per hour. Bus B travels the first one-third of the total time taken at a speed of 40miles per hour, the second one-third at 50 miles per hour and the third one-third at 60 miles per hour. At what distance will the two buses cross each other?

A. 300 miles from M
B. 280 miles from M
C. 305 miles from M
D. 295 miles from M
E. 350 miles from M

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Official Answer

D

A. 300 miles from M
B. 280 miles from M
C. 305 miles from M
D. 295 miles from M
E. 350 miles from M

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IanStewart · Answer

A travels the first third of the distance, or 200 miles, at 40 mph, so that takes 5 hours.

B is traveling at its different speeds for equal amounts of time, so its average speed overall will just be the normal average of its speeds, and it will average (40 + 50 + 60)/3 = 50 mph for the trip, and its total time will thus be 12 hours. So it travels for 4 hours at each speed, and in particular, it travels the first 4 hours at 40 mph, and covers 160 miles, and then travels the next hour at 50 mph, and covers a further 50 miles, so after 5 hours, it has traveled 210 miles.

So after 5 hours, both trains are traveling at 50 mph, and the trains are 190 miles apart. They'll continue to travel at 50 mph until they meet, so now it's just a standard converging speed problem; the distance between the trains is falling at 50+50 = 100 mph, and they are 190 miles apart, so it will take 1.9 hours for the two trains to meet. At 50 mph, each travels 95 miles in 1.9 hours, so in total, train A has traveled 295 miles when they meet, and B has traveled 305 miles. The answer choices all measure the distance from city M, so the question is asking how far A has traveled, and 295 miles is the answer.

Magni03 · Answer

Hi experts , ,need help to understand how to find the distance? i am able to calculate the RS for A& B and the total time taken by each but not able to proceed further. thanks to help

ScottTargetTestPrep · Answer

We need the distance between the point where the busses meet and city M.

I guess you already figured out that bus A is traveling 200 miles at 40 mph, 200 miles at 50 mph, and 200 miles at 60 mph. I also assume that it's clear bus B travels at 40 mph for 4 hours, at 50 mph for 4 hours, and at 60 mph for 4 hours. Since bus A travels 200 miles at 40 mph, it will take bus A 200/40 = 5 hours to travel that portion of its journey. After 5 hours, bus B will have traveled at 40 mph for 4 hours and at 50 mph for 1 hour. Thus, bus B will have traveled 40 * 4 + 50 = 210 miles in total.

Since bus A traveled 200 miles and since bus B traveled 210 miles, the distance between the two busses after 5 hours is 600 - (200 + 210) = 190 miles. In this portion of the journey, both busses are traveling at 50 mph, which means that the distance between the two busses decrease by 100 miles every hour. Thus, the two busses will meet 190/100 = 1.9 hours after bus A traveled 200 miles. Since we need to determine the distance from city M, we need to calculate the total number of miles bus A traveled until the two busses meet. Since bus A travels 200 miles and then travels for 1.9 miles at 50 mph, bus A is 200 + 1.9 * 50 = 295 miles away from city M, which is the distance between the point where two busses meet and city M.

Answer: D

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Cities M and N are 600 miles apart. Bus A starts from city M towards N

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Cities M and N are 600 miles apart. Bus A starts from city M towards N

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