# Quantitative Aptitude- Time,Speed and Distance- A quick result to learn!

PSA_LEVEL-UP_QNR34. Two trains A and B start simultaneously in the opposite direction from two points A and B and arrive at their destinations 9 and 4 hours respectively after their meeting each other. At what rate does the second train B travel if the first train travels at 80 km per hour?

a) 60 km/hr
b) 100 km/hr
c) 120 km/hr
d) 80 km/hr
e) None of these.

Ans: Let us assume M is the point at which trains departing from A and B meet after a time say ‘t’ hrs.

A————————————M—————————————B

Thus,
AM = Sa*t —- (q)   [Sa is the speed of the train departing from A.]
MB= Sb*t —- (r)   [Sb is the speed of the train departing from B.]

Also, according to the question,
(i) train departing from A takes 9 hours to cover distance MB. If speed of this train is Sa, the distance MB is given by 9*Sa.
(ii) similarly train departing from B takes 4 hours to cover distance MA. If speed of this train is Sb, the distance MA is given by 4*Sb.

Comparing AM/MB in both the cases,

AM/MB = Sa/Sb (from equations q and r)
& MA/MB = 4Sb/9Sa

Sa/Sb = 4Sb/9Sa
=>Sa²/Sb² = 4/9   —–(III)
=>Sa/Sb= 2/3
=>Sb= 3Sa/2 = 3*80/2 = 120 km/hr. Option c.

It is worth remembering the equation (III) as a special case of two trains starting from two points moving towards each other, meeting at a particular point and from there taking times ‘t1’ and ‘t2’ respectively to reach the other respective end points. The speed of the these two trains is simply equal to the inverse of square root of the two times t1 and t2.