Question

1) A boat travels 8 km upstream and 32 km downstream in 6 hours. The same boat travels 20 km
upstream and 16 km downstream in 7 hours, find the speed of the boat in still water and the speed
of the stream​

Answer 1

Let speed of boat be x and stream be y.

• upstream = x - y
• downstream = x + y

→ 8/(x - y) + 32/(x + y) = 6

→ 20/(x - y) + 16/(x + y) = 7

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

→ 8u + 32v = 6 __(1)

→ 20u + 16v = 7 __(2)

Multiplying - 2 by (2),

→ - 40u - 32v = - 14 __(3)

By adding (1) and (3),

→ - 32u = - 8

→ u = 1/4

Then, 8(1/4) + 32v = 6

→ v = 1/8

Hence, x - y = 4 and x + y = 8

On adding both we get,

→ x = 6 km/h

Hence, y = 8 - x = 2 km/h.

Speed of boat is still water is 6 km/h and speed of stream is 2 km/h.

Answer 2

• Let speed of boat in still water is x km/hr and speed of boat in stream water is y km/hr.

Then;

Speed of boat in downstream = (x + y) km/hr

Speed of water in upstream = (x - y) km/hr.

We know that..

Time = $\dfrac{Distance}{Speed}$

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» CASE 1)

A boat travels 8 km upstream and 32 km downstream in 6 hours.

→ $\dfrac{8}{x\:-\:y}$ + $\dfrac{32}{x\:+\:y}$ = 6

Let $\frac{1}{x\:-\:y}$ = a and $\frac{1}{x\:+\:y}$ = b

→ 8a + 32b = 6

→ 4a + 16b = 3 ________ (eq 1)

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» CASE 2)

The same boat travels 20 km upstream and 16 km downstream in 7 hours.

→ $\dfrac{20}{x\:-\:y}$ + $\dfrac{16}{x\:+\:y}$ = 7

→ 20a + 16b = 7 __________ (eq 2)

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On multiplying (eq 1) with 5 we get;

→ 20a + 80b = 15 ______ (eq 3)

• Subtract (eq 2) from (eq 3)

→ 20a + 80b - (20a + 16b) = 15 - 7

→ 20a + 80b - 20a - 16b = 8

→ 64b = 8

→ b = 1/8

Put value of of b in (eq 1)

→ 4a + 16(1/8) = 3

→ 4a + 2 = 3

→ 4a = 1

→ a = 1/4

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Now..

→ $\dfrac{1}{x\:-\:y}$ = $\dfrac{1}{4}$ and $\dfrac{1}{x\:+\:y}$ = $\dfrac{1}{8}$

→ x - y = 4 _______ (eq 4)

and

→ x + y = 8 km/hr ________ (eq 5)

• Add (eq 4) and (eq 5)

→ x - y + x + y = 4 + 8

→ 2x = 12

→ x = 6

Put value of x in (eq 5)

→ 6 + y = 8

→ y = 2

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Speed of boat in still water is 6 km/hr and speed of boat in stream water is 2 km/hr.

___________ [ ANSWER ]

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