Question

A motorboat goes downstream on a river and covers a certain distance between two towns in 6 hours. It covers this distance upstream in 8 hours. If the speed of the stream is 2 km/h, find the distance between the two towns.​

Answer 1

Here is your 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= −12−10

∴ −x= −22

x=22

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

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