Two automobiles are 150 kilometers apart and travelling towards each other. One automobile is moving at 60 kmph and the other is moving at 40 kmph. In how many hours will they meet?
Answers
Explanation:
The cars meet after 1.5 hours driving time.
The “average” velocity for “closing time” of two cars going straight towards one another is 60 km/hr + 40 km/hr = 100 km/hr.
[If the two we’re going in the same direction, the average would be 40 km/hr + (60 km/hr - 40 km/hr)/2 = 50 km/hr. And if they were going away from each other in opposite directions, the average “separating” velocity would be 60 km/hr - 40 km/hr = 20 km/hr.]
This average closing velocity 100 km/hr will close the 150 km gap d in
t = d/v(avg)
t = 150 km / 100 km/hr = 1.5 hr.
The car at 60 km/hr travels
d = v•t = 60•1.5 = 90 km.
The car at 40 km/hr travels
d = v•t = 40•1.5 = 60 km.
60 + 90 = 150 km.
By ratios, the velocity 60 is 1.25 times the velocity 40. 1/1.25 = 0.8. There are two shares of 75 km if both cars were driving the same velocity. But by the 1/1.25 ratio, the slower car gets 0.8 share of half the distance:
0.8 • 150 km/2 = 60 km.
The faster car gets the rest, 2 - 0.8 = 1.2 of half the distance:
1.2 • 150/2 = 90 km.
Given that both drive times t(40) and t(60) are the same:
t(40) = 60 km / 40 km/hr = t(60) = 90 km / 60 km/hr = 1.5 hrs.