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A boat covers a distance of 160 m in downstream and 96 m in upstream in 14 seconds and also a distance of 140 m in downstream and 128 m in upstream in 15 seconds. Find the time taken by the boat to cross a 100 m port when the boat is moving in upstream where the length of boat is 44 m.

A boat covers a distance of 160 m in downstream and 96 m in upstream in 14 seconds and also a distance of 140 m in downstream and 128 m in upstream in 15 seconds. Find the time taken by the boat to cross a 100 m port when the boat is moving in upstream where the length of boat is 44 m. Correct Answer 9 seconds

Given:

A boat covers a distance of 160m in downstream and 96m in upstream in 14 seconds

And also a distance of 140m in downstream and 128m in upstream in 15 seconds

Formula used: Distance = Speed × Time, (s = v × t)

Calculation:

Let the speed of boat in still water be x m/s

And let the speed of stream be a m/s

So, the speed of boat in downstream = (x + a) m/s

And the speed of boat in upstream = (x – a) m/s

According to question,

160/(x + a) + 96/(x – a) = 14     ---- (i)

And 140/(x + a) + 128/(x – a) = 15      ---- (ii)

Let 1/(x + a) = u and let 1/(x – a) = v

So, from above equations, we get

160u + 96v = 14      ---- (iii)

140u + 128v = 15      ---- (iv)

From (iii) and (iv), we get

u = 1/20 and v = 1/16

So, (x + a) = 20

And (x – a) = 16

Solving above equations we will get

x = 18 and a = 2

∴ Required time taken = (100 + 44)/16 = 9 seconds.

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