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A boat goes 20 km against the stream and 32 km along the stream in 8 hours. It also goes 32 km against the stream and 20 km along the stream in 8.5 hours. What is the rate of stream?

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A boat goes 20 km against the stream and 32 km along the stream in 8 hours. It also goes 32 km against the stream and 20 km along the stream in 8.5 hours. What is the rate of stream?


1). 0.755 kmph
2). 0.855 kmph
3). 0.84 kmph
4). 1 kmph


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Answered by on | Votes 1 |

Let the rate of upstream be x kmph and rate of downstream be y kmph

⇒ Then, $(\frac{{20}}{x}\; + \;\frac{{32}}{y} = 8)$      .....(1)

⇒ Also, $(\frac{{32}}{x}\; + \;\frac{{20}}{y} = \frac{{17}}{2})$     .....(2)

Adding eq (1) and eq(2), we get

⇒ 52(1/x + 1/y) = 33/2

⇒ $(\frac{1}{x}\; + \;\frac{1}{y} = \frac{{33}}{{104}})$      ......(3)

Subtracting eq (1) from eq(2), we get

⇒ 12(1/x – 1/y) = 1/2

⇒ $(\frac{1}{x}\; - \;\frac{1}{y} = \frac{1}{{24}})$     ......(4)

Adding eq (3) and eq (4), we get

⇒ 2/x = 14/39

⇒ x = 5.57 kmph

⇒ Substitute x in eq (3), we get

⇒ 1/(5.57) – 1/y = 1/24

⇒ y = 7.25 kmph

Upstreamrate is 5.57 kmph and rate downstream is 7.25 kmph

∴ Rate of current = $(\frac{{7.25\; - \;5.57}}{2})$ = 0.84 kmph

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