Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed `u` along the track so that the relative velocities of the trains with respect to the wind are in the ratio `1:2,` then the speed of each train must be

Options

A. 3 u
B. 2 u
C. 5 u
D. 4 u

Answer

A

Explanation

Let the speed of trains be v.

`v_(t_(1)w)=v_(t_(1))-v_(w)=v-u`
`v_(t_(2)w)=v_(t_(2))-v_(w)=(-v)-u= -v-u`
Given, `|v-u|:|-v-u|=1:2`
`therefore (v-u)/(v+u)=(1)/(2) or `
`2v-2u=v+u or v=3u`