Question

A person can row 8 km upstream and 24 km downstream in 4 hours. He can row 12 km downstream and 12 km upstream in 4 hours. Find the speed of the person in still water as also the speed of the current.

Answer 1

Let speed of a boat (that person rows) in still water be x km/h and of stream as y km/h

Then,

→ 8/(x - y) + 24/(x + y) = 4

Let 1/(x - y) be u and 1/(x + y) be v.

→ 8u + 24v = 4

→ 2u + 6v = 1 __(1)

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Similarily,

→ 12u + 12v = 4

→ 3u + 3v = 1 __(2)

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On doing - 3 × (1) and 2 ×(2) we get,

→ - 6u - 18v = - 3 __(3)

→ 6u + 6v = 2 __(4)

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On adding (3) and.(4) we get,

→ - 12v = - 1

→ v = 1/12

So, x + y = 12

→ 6u + 6 × 1/12 = 2

→ 6u = 2 - 1/2

→ u = 3/12 or 1/4

So, x - y = 4

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On adding both bold equations we get,

x = 8 and y = 4

Hence speed of boat is 8 km/h and stream is 4 km/h.

Answer 2

Let speed of a boat (that person rows) in still water be x km/h and of stream as y km/h  

Then,

→ 8/(x - y) + 24/(x + y) = 4

Let 1/(x - y) be u and 1/(x + y) be v.

→ 8u + 24v = 4

→ 2u + 6v = 1 __(1)

______________________________

Similarily,

→ 12u + 12v = 4

→ 3u + 3v = 1 __(2)  

______________________________

On doing - 3 × (1) and 2 ×(2) we get,

→ - 6u - 18v = - 3 __(3)

→ 6u + 6v = 2 __(4)

______________________________

On adding (3) and.(4) we get,

→ - 12v = - 1

→ v = 1/12

So, x + y = 12

→ 6u + 6 × 1/12 = 2

→ 6u = 2 - 1/2

→ u = 3/12 or 1/4

So, x - y = 4  

______________________________

On adding both bold equations we get,  

x = 8 and y = 4

Hence speed of boat is 8 km/h and stream is 4 km/h.