Two train stations are apart by 1.10 miles (1770 m). Accidently, two trains are

Question

Two train stations are apart by 1.10 miles (1770 m). Accidently, two trains are sent on a collision course onto the same track connecting the stations. Both trains start at rest, accelerating at a constant rate, the eastbound train at 0.35 m/s2 and the westbound train at 0.85 m/s2.
a) What distance does the eastbound train travel before the collision?
b) What is the speed of the westbound train just before the collision?

The answer to a & b are 516 m and 46.7 m/s.

The answers are not the issue, it's the method of arriving to it. The problem solving steps I was given was very complicated and was wondering if someone could give me a more easier way of solving.

Explanation / Answer

Relative acceleration of the train=acc. of east bound train +acc. of westbound train [since they are moving in opposite direction.

arel=0.35+0.85=1.20 m/s2

distance covered in total=1770m

urel t+0.5arelt2=1770

0t+0.5*1.20*t2=1770

t=54.31 sec

a. Distance covered by eastbound train=0.5at2=0.5*0.35*54.312=516.25m

b. Speed of westbound train, v=u+at=0+0.85*54.31=46.17 m/s

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