Question

A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours. In
a
the same time it covers a distance of 12 km upstream and 36 km downstream. Find the
speed of the boat in stil water and that of the stream
​

Answer 1

Question :-

• A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36 km downstream. Find the speed of the boat in stil water and that of the stream.

Answer :-

Let speed of the boat in still water = x km/hr, and

Speed of the stream = y km/hr

Downstream speed = (x+y) km/hr

Upstream speed = (x−y) km/hr

Case :- 1.

A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours.

Time taken to cover a distance of 16 km with (x - y) km/hr

$\bf\implies \:\dfrac{16}{x - y} \: hours$

Time taken to cover a distance of 24 km with (x + y) km/hr

$\bf\implies \:\dfrac{24}{x + y} \: hours$

Since, total time taken = 6 hours.

$\bf\implies \:\dfrac{16}{x - y} + \dfrac{24}{x + y} = 6......(1)$

Case :- 2.

A motorboat covers a distance of 12 km upstream and 36 km downstream in 6 hours.

Time taken to cover a distance of 12 km with (x - y) km/hr

$\bf\implies \:\dfrac{12}{x - y} \: hours$

Time taken to cover a distance of 36 km with (x + y) km/hr

$\bf\implies \:\dfrac{36}{x + y} \: hours$

Since, total time taken = 6 hours.

$\bf\implies \:\dfrac{12}{x - y} + \dfrac{36}{x + y} = 6.....(2)$

$\bf \:Let \: \dfrac{1}{x - y} = v \: and \: \dfrac{1}{x + y} = u$

So, equation (1) can be rewritten as

$\bf\implies \:24u+16v=6$

$\bf\implies \:12u+8v=3 ....... (3)$

Equation (2) can be rewritten as

$\bf\implies \:36u+12v=6$

$\bf\implies \:6u+2v=1 ........... (4)$

Multiplying (4) by 4, we get,

$\bf\implies \:24u+8v=4 .....… (5)$

On, Subtracting (3) by (5), we get,

$\bf\implies \:12u=1$

$\bf\implies \:u = \dfrac{1}{12} .....(6)$

Putting the value of u in (4), we get,

$\bf\implies \:6 \times \dfrac{1}{12} + 2v = 1$

$\bf\implies \:v = \dfrac{1}{4}$

So, it means,

$\bf\implies \:\dfrac{1}{x + y} = \dfrac{1}{12} \: and \: \dfrac{1}{x - y} = \dfrac{1}{4}$

$\bf\implies \:x + y = 12 \: ....(7)$

$\bf\implies \:x - y = 4.....(8)$

On adding (7) and (8), we get

$\bf\implies \:2x = 16\bf\implies \:x = 8 \: km/hr$

On subtracting (7) and (8), we get

$\bf\implies \:2y = 8\bf\implies \:y = 4 \: km/hr$

Thus, speed of the stream = 4 km/hr

Speed of the boat in still water = 12 km/hr

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Additional Information:-

Stream – The moving water in a river is called stream.

Upstream – If the boat is flowing in the opposite direction to the stream, it is called upstream. In this case, the net speed of the boat is called the upstream speed. 

Downstream – If the boat is flowing along the direction of the stream, it is called downstream.