Question

Two trains leave the same train station at the same time, moving along straight tracks that form 35 angle. If one train travels at an average speed of 100 mi/hr and the other at an average speed of 90 mi/hr, how far apart are the trains after 30 min?

Answer 1

Trains are `28.96` miles apart after `30` minutes.

Explanation:

The train with `100` mi/hr has moved in `30` min `100/(30/60)= 50`miles
The train with `90` mi/hr has moved in `30` min `90/(30/60)= 45`miles.
So this may be regarded as a triangle of which sides are `a=50 ; b=45` and their included angle is `/_C=35^0`

by applying cosine law, `c^2=a^2+b^2-2ab cosC or c^2= 50^2+45^2-2*50*45*cos35=2500+2025+4500*0.82=838.82(2dp)`
`c= sqrt 838.82=28.96` miles.

The trains are `28.96` miles apart after `30` minutes. [Ans]