Question

boat goes 16 km upstream and 24 km downstream in 6 hours. Also it covers 12 km upstream
and 36 km downstream in the same time. Find the speed of the boat upstream and downstream.
​

Answer 1

Step-by-step explanation:

Let upstream speed = x km/h

And Downstream speed = y km/h

Time taken to cover 16 km in upstream

= 16/x h

Time taken to cover 24 km in downstream

= 24/y h

Total time taken = 6 h

=> upstream time +downstream time = 6h

=> 16/x + 24/y = 6h

=> 2(8/x +12/y) = 6

=> 8/x + 12/y = 3 —----(1)

Again,

Time taken to cover 12 km in upstream

= 12/x h

Time taken to cover 36 km in downstream

= 36/y h

Total time taken = 6 h

=> 12/x + 36/y = 6

=> 6(2/x + 6/y) = 1

=> 2/x + 6/y = 1 - - - - (2)

From equation (1)×1 - (2)×2, we get

8/x + 12/y =3

4/x + 12/ y = 2

-----------------------

8/x - 4/x =3- 2

=> 8 - 4/x = 1

=> 4/x = 1

=> x = 4 km/h

Now, putting the value of x in equation (2)

2/4 +6/y = 1

=> 1/2 + 6/y = 1

=>6/y = 1- 1/2

=> 6/y = 2-1/2

=> 6/y = 1/2

=> y = 6×2

=> y = 12 km/ h

Hence, upstream speed = 4 km/h

Downstream speed = 12 km/h ANS.