Question

Abdul travelled 300 km by the train and 200 km by taxi . It took him 5 hours and 30 minutes but if he travelled 260 km by train and 240 km by taxi he takes 6 mins longer . Find the speed of train and that of taxi.

Answer 1

let speed of train = x km / min

speed of taxi = y km / min

so . according to first condition ,

time taken is ,

300/x + 200/y = 330

30/x + 20/y = 33

20x + 30y = 33xy -------(1)

according to second condition ,

260/x + 240/y = 336

65/x + 60/y = 84

60x + 65y = 84xy -------(2)

eq 1 can be write as

60x + 90y = 99xy -------(3)

subtracting 2 from 3

25y = 15xy

x = 25 /15

x = 5/3 km/min

x = 27.77 meter/second

putting x = 5/3 in above

we get

60x + 65y = 84xy

60 × 5/3 + 65y = 84 × 5/3 × y

100 + 65y = 140y

75y = 100

y = 100/75

y = 5/4 km/min

y = 20.83 meter/second