Question

A motorboat whose speed is 18 km per hour in still water takes 1 hour more to go 24 km upstream then to return downstream to the same spot find the speed of stream

Answer 1

Answer:

Step-by-step explanation:

Let the speed of stream be x km / hr

For upstream = ( 18 - x ) km / hr

For downstream = ( 18 + x ) km / hr

A.T.Q.

24 / 18 - x - 24 / 18 + x = 1

48 x = 324 - x²

x² + 48 x - 324 = 0

( x + 54 ) ( x - 6 ) = 0

x = - 54 or x = 6

Since speed can't be negative .

Therefore , speed of the stream is 6 km / hr .

Answer 2

Answer:

• The speed of the stream is 6 km/h.

Given :

• Speed of motorboat is 18 km/h

• Time taken 1 hour more to go 24 km.

To find :

• The speed of the stream =?

Step-by-step explanation:

Let the speed of the stream be x km/h. Then,

The speed of the boat downstream = (18 - x) km/h

And the speed of the boat downstream = ( 18 + x) km/h

Time taken to go upstream 24 km = (24/18 - x) hours

And time taken to go downstream 24 km = (24/18 + x) hours.

According to the question,

⟹ (24 / 18 - x) - (24 /18 + x) = 1

⟹ 24(18+x)-24(18-x)/(18-x)(18+x)=1

⟹ 432 + 24x - 432 + 24x = (18)² - (x) ²

⟹ 48x = 324 - x²

⟹ x² + 48x - 324 = 0

⟹ x² + 54x - 6x - 324 = 0

⟹ x(x + 54) - 6(x + 54) = 0

⟹ (x + 54)(x-6)=0

⟹ x = - 54 or x = 6

But the speed cannot be negative.

∴ x = 6

Hence, the speed of the stream is 6 km/h