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A motor boat covers a certain distance downstream in a river in 5 hrs. It covers the same distance upstream in 5.5 hrs. The speed of the water is 1.5

km/hr. The speed of the boat in still water is ?????


Let the speed of boat in still water be  x^{} km/hr.
Speed of water = 1.5 km/hr.

As we know that speed of boat downstream is (x+y) km/hr and speed of boat upstream is (x-y) km/hr.

{Here x means speed of boat in still water and y means speed of the stream}

Now,in this question;
Speed upstream = (x-1.5) km/h
And speed downstream = (x+1.5) km/hr

We know that;
                         Distance = Speed × Time
When boat goes upstream,
 Distance = (x-1.5)(5.5)
                  ⇒ 5.5x - 8.25
When boat goes downstream,
 Distance = (x+1.5)(5)
                 ⇒ 5x + 7.5

Now,while going upstream and downstream, distance is same.
∴ 5.5x - 8.25 = 5x + 7.5
∴ 5.5x - 5x = 7.5 + 8.25
∴ 0.5x = 15.75
∴ x = 31.5

Hence, Speed of the boat in still water is 31.5 km/hr.

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