Question

will it require the same time for a launch to cover a distance of 1km up and down a river (the speed of the water current is 2km/h) and on a lake (in stagnant water) if the speed of the launch relative to the water is 8km/h in both case. if the answer is negative then find the ratio between them ​

Answer 1

ANSWER

⇒ Let x be the speed of the stream.

⇒ Speed of the boat in still water is 8km/hr

⇒ The speed of the boat in upstream is 8−xkm/hr

⇒ The speed of the boat in downstream is 8+xkm/hr

⇒ The time taken by the boat to cover 15km=

8−x

15

hr

⇒ The time taken by the boat to cover 22km=

8+x

22

hr

According to the question,

⇒

8−x

15

+

8+x

22

=5

⇒ 15(8+x)+22(8−x)=5(8−x)(8+x)

⇒ 120+15x+176−22x=5(64−x

2

)

⇒ 296−7x=320−5x

2

⇒ 5x

2

−7x−24=0

⇒ 5x

2

−15x+8x−24=0

⇒ 5x(x−3)+8(x−3)=0

⇒ (x−3)(5x+8)=0

⇒ x−3=0 and 5x+8=0

⇒ x=3 and x=−

5

8

Speed cannot be negative.

∴ The speed of the stream is 3km/hr