Two cars A and B start from Boston and New York respectively simultaneously and travel towards each ...
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 100 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
Answer/Solution
2 hours 40 minutes
Steps/Work
Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/100)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 100 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (100+60)=160 minutes on the road.
E. 2 hours 40 minutes
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/100)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 100 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (100+60)=160 minutes on the road.
E. 2 hours 40 minutes