# Mathematics

A car traveling at an average speed of 55 kph leaves Town A for Town B, at a distance of 120 km. At the same time, another car, traveling on the same highway at an average speed of 45 kph, leaves Town B for Town A. How many hours will they meet? How far from Town A will they meet?

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1. Their combined speed is 100 km/hr
distance = speed * time, so they will meet in
120/100 = 6/5 hours.
So, how far will A go in that time?

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oobleck
2. Let the distance from A to the meeting point be x km
then the distance from B to the meeting point is 120-x km

time from point A = x/55
time from point B = (120-x)/45
but those two times must be equal, they both left at the same time.

x/55 = (120-x)/45
cross-multiply
45x = 6600 - 55x
100x = 6600
x = 66

They will meet 66 km from town A
the time will be x/55 or 66/55 = 6/5 hrs
which is 1 hour and 12 minutes

(notice I would get the same time if I had used
(120-x)/45
= (120-66)/45
= 54/45
= 6/5

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