Question

A freight train and a passenger train leave the same stations at noon and travel in opposite directions. If the freight train travels 52mph and the passenger train travels 84mph, at what time are they 680 miles apart?

Answer 1

Hint: The idea is of relative speed is simple to understand, and we mainly need to know the working of the concept in the following cases
Two bodies moving in the same direction
Two bodies moving in the opposite direction
If two objects are moving with speeds X and Y, their relative speed is
X + Y, if they are moving in the opposite direction………………….(1)
X – Y, if they are moving in the same direction. ………………….(2)

Complete step-by-step answer:
As the trains are moving in the opposite directions we will use the formulae (1) mentioned in the hint.
Speed of the freight train = $52mph$
Speed of the passenger train = $84mph$
So, the relative speed =$52 + 84 = 136mph$
The distance travelled relatively =$680miles$
We will use the distance formula to calculate time
i.e. Distance = Speed X Time
Therefore the time taken is $ = \dfrac{{dis\tan ce}}{{speed}} = \dfrac{{680}}{{136}} = 5hours$

Note: When two trains are moving in the same direction, then their speed will be subtracted. When two trains are moving in opposite directions, then their speed will be added. In both the above cases, the total distance is the sum of the length of both the trains if given in the question.