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Home » 1. The speed of a boat in still water is km/hr. It can go km upstream and km downstream in hours. Find the speed of the stream.
1. The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Class 10 | ICSE | Maths | Quadratic Equations | RD Sharma
1. The speed of a boat in still water is 8km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.

Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring.

Solution:

Let the speed of stream be x km/hr

Given, speed of boat in still water is 8km/hr.

So, speed of downstream =\left( 8+x \right) km/hr

And, speed of upstream =\left( 8-x \right) km/hr

Using, speed = distance/ time

Time taken by the boat to go 15 km upstream =15/\left( 8-x \right)hr

And, time taken by the boat to return 22 km downstream =22/\left( 8+x \right)hr

From the question, the boat returns to the same point in 5 hr.

so, \frac{15}{\left( 8-x \right)}+\frac{22}{\left( 8+x \right)}=5

\frac{15\left( 8+x \right)+22\left( 8-x \right)}{\left( 8-x \right)\left( 8+x \right)}=5

\frac{120+15x+176-22x}{64+{{x}^{2}}}=5

\frac{296-7x}{64-{{x}^{2}}}=5

5{{x}^{2}}-7x+296-320=0

5{{x}^{2}}-7x-24=0

5{{x}^{2}}-15x+8x-24=0 [by factorisation method]

5x\left( x-3 \right)+8\left( x-3 \right)=0

\left( x-3 \right)\left( 5x+8 \right)=0

\therefore x=3,x=-8/5

As the speed of the stream can never be negative, only the positive solution is considered.

Therefore, the speed of the stream is 3 km/hr.

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