Question

A passenger train leaves New Delhi at 5 pm, followed by a goods train, which leaves the station at 7 pm. The goods train travels 20 km/h faster than the passenger train. The goods train arrives at a station, 1040 km away, 2 hours 36 minutes before the passenger train. Calculate their speeds.

Answer 1

Let the speed of the passenger train be x km/h
Let the speed of the goods train be (x+20)km/h
Distance travelled by both trains = 1040 km
Time taken by passenger train = $\frac{1040}{x}$
Time taken by goods train = $\frac{1040}{x+20}$
As per the question,
Goods train arrived 2 hours 36 minutes before the passenger train
$\frac{1040}{x+20} = \frac{1040}{x} - 2 \frac{36}{60}$
$\frac{1040}{x+20} = \frac{1040}{x} - \frac{13}{5}$ 
$\frac{1040}{x+20} = \frac{5200-13x}{5x}$ 
Cross multiplying and simplifying, we get

x²+20x-8000=0
On solving this quadratic equation, we get x = 80

So, Speed of the passenger train = 80 km/h
The speed of the goods train = 100 km/h