M4maths Previous Puzzles

24 Jul 2013 Problem

Two trains leave a railway station at the same time. The first train travels due west and the second train travels due north. The first train travels 5 km/hr faster than the second train. If after two hours, they are 50 km apart, find the speed of first train.

OPtion

1) 10 km/hr
2) 15 km/hr
3) 20 km/hr
4) 25 km/hr
5) 30 km/hr
6) 35 km/hr
7) 40 km/hr
8) 45 km/hr
9) 50 km/hr
10) None of these

Solution

Let the speed of the second train = x km/hr
The speed of the first train = x+5 km/hr
Distance covered after two hours by the first train is 2(x+5) km.
Distance covered by the second train after two hours is 2x km.
(2x)^2 + 4(x+5)^2=(50)^2 (Using pythagoras theorem)
Solve
We get x=-20 and x=15
The speed of the first train = 15+5=20km/hr
option 3

Correct Option: 3 Best Solution (0)