Question

a motorboat goes downstream in the river and covers the distance between two coastal towns in 3 hours. It covers this distance upstream in 4 hours. If the speed of the stream is 5 km/hr , find the speed of the boat in still water and the distance between the two coastal towns

Answer 1

Let the speed of the boat in still water = xkm/hrxkm/hrSpeed of the boat downstream =(x+3)km/hr=(x+3)km/hrTime taken to cover the distance = 5 hrsDistance covered in 5 hrs =(x+3)×5=(x+3)×5Speed of the boat up stream =(x−3)km/hr=(x−3)km/hrTime taken to cover the distance = 6 hrsDistance covered in 5 hrs =6(x−3)=6(x−3)Distance between two coastal towns is fixed .According to the question=> 5(x+3)=6(x−3)5(x+3)=6(x−3)=> 5x+15=6x−185x+15=6x−18=> −x=−33−x=−33x=33x=33Required speed of the boat is 33km/hr33km/hrAnswer : 33km/hr

Answer 2

Answer:

Since we have to find the speed of the boat in

still water, let us suppose that it is

x km/h.

This means that while going downstream the

speed of the boat will be (x + 2) kmph

because the water current is pushing the boat

at 2 kmph in addition to its own speed

‘x’kmph.

Now the speed of the boat down stream = (x + 2) kmph

⇒ distance covered in 1 hour = x + 2 km.

∴ distance covered in 5 hours = 5 (x + 2) km

Hence the distance between A and B is 5 (x + 2) km

But while going upstream the boat has to work against the water current.

Therefore its speed upstream will be (x – 2) kmph.

⇒ Distance covered in 1 hour = (x – 2) km

Distance covered in 6 hours = 6 (x – 2) km

∴ distance between A and B is 6 (x – 2) km

But the distance between A and B is fixed

∴ 5 (x + 2) = 6 (x – 2)

⇒ 5x + 10 = 6x – 12

⇒ 5x – 6x = –12 – 10

∴ –x = –22

x = 22.

Therefore speed of the boat in still water is 22 kmph.