# A Motor Boat Whose Speed in Still Water is 18 Km/Hr Takes 1 Hour More to Go 24 Km up Stream that to Return Down Stream to the Same Spot. Find the Speed of the Stream. - Mathematics

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

#### Solution

Let the speed of the stream be x km/hr.
speed of the boat in still water = 18 km/hr.
Total Distance = 24 km.
We know that,
Speed of the boat up stream = speed of the boat in still water − speed of the stream
= (18 − x) km/hr
Speed of the boat down stream = speed of the boat in still water + speed of the stream
= (18 + x) km/hr
Time of up stream journey = t1 = $\frac{24}{18 - x}$

Time of down stream journey = t2 = $\frac{24}{18 + x}$

According to the question,
t1 − t2 = 1 hr

$\Rightarrow \frac{24}{18 - x} - \frac{24}{18 + x} = 1$

$\Rightarrow \frac{24(18 + x - 18 + x)}{(18 - x)(18 + x)} = 1$

$\Rightarrow \frac{24(2x)}{(18 )^2 - x^2} = 1$

$\Rightarrow 48x = 324 - x^2$

$\Rightarrow x^2 + 48x - 324 = 0$

$\Rightarrow x^2 + 54x - 6x - 324 = 0$

$\Rightarrow x(x + 54) - 6(x + 54) = 0$

$\Rightarrow (x - 6)(x + 54) = 0$

$\Rightarrow x - 6 = 0 \text { or } x + 54 = 0$

$\Rightarrow x = 6 \text { or } x = - 54$

Since, speed cannot be negative.
Thus, speed of the stream is 6 km/hr.

Concept: Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
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#### APPEARS IN

RD Sharma Class 10 Maths
Exercise 4.8 | Q 14 | Page 59