Speed of boat in still water is 15 km hr

Asked by admin @ 05/08/2021 in Math viewed by 292 People

the speed of a boat in still water is 15 km / hr . it can go 30 km upstream and return downstream to the orginal point in 4 hours and 30 minutes . find the speed of the stream .

Answered by admin @ 05/08/2021

Solution :-

Let the speed of the train be x km/h.

Downstream speed = (15 + x) km/h

Upstream speed = (15 - x) km/h

Time taken to go 30 km upstream = 30/(15 - x) hrs.

Time taken to go 30 km downstream = 30/(15 + x) hrs.

According to the Question,

⇒ 30/(15 - x) + 30/(15 + x) = 9/2

⇒ 30(15 + x) + 30(15 - x)/(15 + x) (15 - x) = 9/2

⇒ 450 + 30x + 450 - 30x/225 - x² = 9/2

⇒ 900/225 - x² = 9/2

By cross-multiplication, we get

⇒ 9(225 - x²) = 1800

⇒ 225 - x² = 200

⇒ x² = 25

⇒ x = ± 5

(As speed can't be negative)

⇒ x = 5 km/h

Hence, the speed of stream is 5 km/h.

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