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A steamer with speed 15 km/h in still water travels 40 km downstream and returns in 6 hr. What is the Speed of Current?
- A5 km/h
- B4.5 km/h
- C6 km/h
- D5.5 km/h
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CCommunity
Let, Speed of the Current = y km/h
∴ Downstream speed = (15 + y) km/h
⇒ Upstream Speed = (15 - y) km/h
∴ Time needed to travel 40km downstream = 40/(15 + y) hr.
∴ Time needed to travel 40km upstream = 40/(15 - y) hr.
According to problem,
$(\frac{{40}}{{15\; + \;y}}\; + \;\frac{{40}}{{15 - y}})$ = 6
Or, 1200/(225 - y2) = 6
Or, 1200 = 1350 - 6y2
Or, 6y2 = 150
Or, y2 = 25
⇒ y = 5
∴ Speed of the stream = 5 km/h
∴ Downstream speed = (15 + y) km/h
⇒ Upstream Speed = (15 - y) km/h
∴ Time needed to travel 40km downstream = 40/(15 + y) hr.
∴ Time needed to travel 40km upstream = 40/(15 - y) hr.
According to problem,
$(\frac{{40}}{{15\; + \;y}}\; + \;\frac{{40}}{{15 - y}})$ = 6
Or, 1200/(225 - y2) = 6
Or, 1200 = 1350 - 6y2
Or, 6y2 = 150
Or, y2 = 25
⇒ y = 5
∴ Speed of the stream = 5 km/h