Question

17. A motor boat takes 2 h to travel a distance
of 9 km down the current and it takes 6 h
to travel the same distance against the
current. The speed of the boat in still water
and that of the current (in km/h)​

Answer 1

SOLUTION :-

Let the velocity of boat in still water be 'x' and velocity of water current be 'y'.

CASE - 1

★ For downstream ,

Speed of boat will be (x+y)km/hr.

Time taken is 2hrs.

Distance is 9km.

We know , Speed = Distance/Time

x+y = 9/2 ————— (i)

CASE - 2

★ For upstream ,

Speed of boat will be (x-y)km/hr.

Time taken is 6hrs.

Distance is 9km.

By applying same formula ,

x-y = 9/6 ————— (ii)

________________________

Adding equation (i) and (ii) , we get..

→ x+y+x-y = (9/2)+(9/6)

→ 2x = (27+9)/6

→ 2x = 36/6

→ 2x = 6

→ x = 3

Putting x=3 in eqⁿ (i) ,

→ x+y = 9/2

→ 3+y = 9/2

→ y = (9/2) - 3

→ y = 3/2

Hence , speed of boat in still water is 3km/hr and speed of water current is 3/2 km/hr.