Question

The speed of the boat in still water is 10 km/h. If it can travel 26 km upstream in the same time, find the speed of the stream.

Answer 1

Solution

Let the speed of stream = x Km/h

Since, speed of boat in still water = 10 km/h

∴ Speed of boat in downstream = ( x + 10 ) Km/h

and speed of boat in upstream = ( 10 - x )

∴ Time taken to travel 26 km upstream =  $\frac{26}{10+x} hr$

Time taken to travel 14 km upstream = $\frac{14}{10-x} hr$

According to given condition,

$\frac{26}{10+x} hr$ =  $\frac{14}{10-x} hr$

26( 10 - x ) = 14 ( 10 + x )

⇒ 260 - 26x  = 140 + 14x

⇒           40x = 120

⇒               x = 3 km / hr Answer

 

Answer 2

Question:

The speed of the boat in still water is 10 km/h. If it can travel 26 km downstream and 14 km upstream at the same time, find the speed of the stream.

Solution:

Let the speed of the stream = x km/h

Given:

The speed of boat in still water = 10Km/h

Upstream Distance = 14 Km

Downstream Distance = 26 Km

Upstream speed = (10 - x) Km/h

Downstream Speed = (10 + x) Km/h

We know,

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

Upstream Time (in hours)= $\dfrac{14}{10 - x}$

Downstream Time (in hours) = $\dfrac{26}{10 + x}$

According to question

Time taken by boat to travel upstream = Time taken by the boat to travel downstream

$\implies \dfrac{14}{10 - x} = \dfrac{26}{10 + x}$

$\implies \dfrac{7}{10 - x} = \dfrac{13}{10 + x}$

$\implies 13(10 - x) = 7(10 + x)$

$\implies 130 - 13x = 70 + 7x$

$\implies 130 - 70 = 7x + 13x$

$\implies x = \dfrac{60}{20}$

$\implies x = 3$

Hence, the speed of the stream in 3 Km/h.