Question

Abdul travelled 300km by train and 200 km by taxi taking 5 hour's 30 minutes. But ,if he travelled 260 km by train and 240 km by taxi, he takes 6 minutes longer.Find the speed of the train and that of the taxi.

Answer 1

Hope this helps you.
Thanks

Answer 2

Hii friend,

Let the speeds of the train and taxi be X km/hr and Y km/hr respectively. Then,

Time Taken to cover 300 km by train = 300/X hrs.

And,

Time Taken to cover 200 km by taxi = 200/Y hrs.

Total Time Taken = 5 30/60 hrs = 5 1/2 hrs = 11/2 hrs.

Therefore,

300/X + 200/Y = 11/2

2(300/X +200/Y) = 11

600/X + 400/Y = 11.........(1)

Let 1/X = U and 1/Y = V

Then equation (1) become,

600U + 400V = 11......(2)

Again,

Time Taken to cover 260 km by train = 260/X hrs.

And,

Time Taken to cover 240 km by taxi = 240/Y hrs.

Total time taken = 5 36/60 hrs = 5 3/5 = 28/5 hrs.

Therefore,

260/X +240/Y = 28/5

5(260/X +240/Y) = 28

1300/X + 1200/Y = 28

1300U +1200V = 28......(3)

On multiplying (2) by 3 and subtracting (3) from it , we get:

1800U + 1200V = 24

1300U + 1200V = 33
_________________

500U = 5

U = 5/500 = 1/100

On putting U = 1/100 in (2), we get:

( 600×1/100) + 400V = 11

400V = 5

V = 5/400= 80

Now,

U = 1/100 => 1/X = 1/100 = X = 100

V = 1/80 => 1/Y = 1/80 = Y = 80

Therefore,

Speed of the train = 100 km/hr

And,

Speed of the taxi = 80 km/hr.

HOPE IT WILL HELP YOU..... :-)