It took a crew 2 hours 40 minutes to row 6 km upstream and back again. If the rate of flow of the stream was 3 km/h, what was the rowing speed of the crew in still water?

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Answer 1 · 2018-05-30T11:31:28

Rowing speed in steel water is #6# km/ hour.

Let the rowing speed in steel water be #x# km/ hour

Rowing speed in upstream is #x-3# km/ hour

Rowing speed in downstream is #x+3# km/ hour

Total time taken is #2# hrs #40# minutes i.e #2 2/3#hour

to cover up and down journey of #12# Km

# :. 6/(x-3) + 6/(x+3)=8/3# Multiplying by #3(x^2-9)# on both

sides we get, # 18(x+3) + 18(x-3)=8(x^2-9)# or

# 8 x^2-36 x -72=0 or 2 x^2 - 9 x -18=0# or

#2 x^2 - 12 x +3 x-18=0# or

#2 x( x-6)+3(x-6)=0 or (2 x +3)(x-6)=0#

#:.x= 6 or x =-3/2 ; x != -3/2 :. x =6# km/hr

Rowing speed in steel water is 6 km/ hour [Ans]