Question

Two train leave a railway station at same time. The first train travels due west and second train due north . The first train travels 5km/h faster than the second train . If after 2 hours they are 50km apart find the average speed of each train

Answer 1

let say speed of first train = s km /hr

distance covered in 2 hr =2s km

towards West

speed of second train = s -5 km/hr

as speed of first train is 5 km higher

distance covered in 2hr = 2(s-5)

= 2s - 10 km towards north

as one train goes towards west and another goes north

so distance is Northwest = 50 km

north and west perpendicular to each other

so using Pythagoras theorem

${(2s)}^{2} + {(2s - 10)}^{2} = {(50)}^{2} \\ \\ 4 {s}^{2} + {4s}^{2} + 100 - 40s = 2500 \\ \\ 8 {s}^{2} - 40s - 2400 = 0$

dividing both sides by 8

${s}^{2} - 5s - 300 = 0 \\ \\ {s}^{2} - 20s + 15s - 300 = 0 \\ \\ s(s - 20) + 15(s - 20) = 0$

(s+15)(s-20) = 0

s = 20 km / hr

speed of faster train = 20 km/hr

speed of slower train = 20-5 = 15 km/hr

Answer 2

Step-by-step explanation:

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