A fast local train takes 30 minutes less than a slow local train for a journey of 60 km. If the speed of the slow local train is 20 km/h less than the speed of the fast local train, what is the speed of the slow local train?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 40 km/h.
Formula Used:
Distance = Speed × Time
Explanation:
Let, the speed of the slow local train be x km/hr then,
The speed of the fast local train will be (x + 20) km/hr
Time taken by the slow train to cover 60 km = 60/x and,
Time taken by the fast train to cover 60 km = 60/(x + 20)
Now,
⇒ 60/x - 60/(x + 20) = 1/2
⇒ 60(1/x - 1/(x + 20)) = 1/2
⇒ 1/x - 1/(x + 20) = 1/120
⇒ (x + 20 - x)/x(x + 20) = 1/120
⇒ 20/(x2 + 20x) = 1/120
⇒ 2400 = x2 + 20x
⇒ x2 + 20x - 2400 = 0
⇒ x2 + 60x - 40x - 2400 = 0
⇒ x(x + 60) - 40(x + 60) = 0
⇒ (x - 40)(x + 60) = 0
⇒ x = 40, - 60 [Speed can not be negative]
So, the speed of the slow local train = 40 km/hr