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?**

150km (see explanation)

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**

## Comments

Sign uporlog in with Facebookto comment.Tarun245150 km \

Tarun245sorry i meant 300 km