Question

A fast train takes 1 hour less than a slow train for a journey of 96 km. If the speed of the slow train is 8 km/h less than that of the fast train, then find the speeds of the fast train and slow train respectively.

• A. 26 km/hr , 34 km/hr
• B. 32 km/hr , 24 km/hr
• C. 34 km/hr , 28 km/hr
• D. 12 km/hr , 14 km/hr

Answer 1

Answer:

B. 32 km/hr , 24 km/hr

Let the speed of the fast train be (x) km/h.
Then speed of the slow train = (x - 8) km/h

Time taken = Distance / Speed

Fast train time = (96/x)
Slow train time = (96/(x - 8))

Given: slow train takes 1 hour more
$\frac{96}{x - 8} = \frac{96}{x} + 1$
Multiply both sides by (x(x - 8)):

$96x = 96(x - 8) + x(x - 8)$
$96x = 96x - 768 + x^2 - 8x$
$0 = x^2 - 8x - 768$
$x^2 - 8x - 768 = 0$
$x = \frac{8 \pm \sqrt{64 + 3072}}{2}$
$= \frac{8 \pm \sqrt{3136}}{2}$
$\sqrt{3136} = 56$
$x = \frac{8 + 56}{2} = 32$

So,
Fast train speed = 32 km/h
Slow train speed = (32 - 8 = 24) km/h

Answer: 32 km/h and 24 km/h