Please solve the 7th question.
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Q.7. A goods train leaves a station at 6 p.m., followed by an express train which leaves at 8 p.m. and travels 20 km/hour faster than the goods train. The express train arrives at a station, 1040 km away, 36 minutes before the goods train. Assuming that the speeds of both the trains remain constant between the two stations; Calculate their speeds.

Express trains is 20 km/hr faster than goods train. Let speed of the express train and goods train be ( x + 20 ) km/hr and x km/hr respectively Let time taken by the goods train = t hours Then, time taken by the express train = ( t − 2 − 36 60 ) hours = ( t − 13 5 ) hours goods train travels 1040 km in t hours with a speed of x km/hr => x t = 1040 ⋯ ( 1 ) express train travels 1040 km in ( t − 13 5 ) hours with a speed of ( x + 20 ) km/hr ⇒ ( x + 20 ) ( t − 13 5 ) = 1040 ⇒ ( x + 20 ) ( 5 t − 13 ) 5 = 1040 ⇒ ( x + 20 ) ( 5 t − 13 ) = 5200 ⇒ 5 x t − 13 x + 100 t − 260 = 5200 ⇒ 5 x t − 13 x + 100 t = 5460 ⋯ ( 2 ) From (1) we have x t = 1040 and t = 1040 x . Using these values in (2) 5 × 1040 − 13 x + 100 × 1040 x = 5460 5200 − 13 x + 104000 x = 5460 − 13 x + 104000 x = 260 − 13 x 2 + 104000 = 260 x 13 x 2 + 260 x − 104000 = 0 x 2 + 20 x − 8000 = 0 ( x + 100 ) ( x − 80 ) = 0 x = 80 Speed of the goods train = x = 80 km/hr Speed of the express train = (x+20) = 100 km/hr