Two Trains Like 7

Two trains (Train A and B) with 200 km between them are travelling towards each other at 100km/h. A mosquito, initially standing on the front of Train A, starts travelling towards Train B at 150km/h. Once it reaches Train B, it turns around and travels towards Train A. The mosquito continues going back and forth between Train A and B until they collide.

How far does the mosquito travel before getting squashed between the two trains when the collide?

Show Answer

150km (see explanation)

Show Solution

The trains will collide in 1 hour since they are both travelling at 100km/h and there's 200km between them. This can be obtained by solving 100T = 200 - 100T, obtaining T = 1. Therefore, the mosquito will be travelling at 150km/h for a total of 1 hour, so it will travel 150km.

Alternatively, solve it in the brute force method:

t1 = time when mosquito reaches Train B

150 x t1 = 200 - 100 x t1

t1 = 4/5

At this point, both trains have travelled 80km (0.80h x 100km/h) so they are 40km apart (200km - 2 x 80km).

t2 = time when mosquito reaches Train A

150 x t2 = 40 - 100 x t2

t2 = 4/25

Similarly, t3 = 4/125, t4 = 4/625, ... , tn = 4/(5^n)

Summing the infinite series of speed x time for the mosquito: 150 [km/h] x sum(n=1 to inf){ 4/(5^n)} [h] = 150km