A motorboat whose speed is 27 km/h in still water takes 20 minutes more to go 40 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 3 km/h, then how much time will it take to go 44 km downstream and 54 km upstream ?
Let speed of the stream=x km/h, then Downstream speed=(27+x) km/h and Upstream speed=(27-x) km/h
Difference of time for 40 km upstream & downstream = 40/(27-x) - 40/(27+x) = 1/3 hrs.
⇒ x² + 240x - 729 = 0
(x+243) (x-3) = 0
x=3 km/h
Now, new speed of a boat in still water=27+3=30 km/h
.'. Downstream speed=(30+3)=33 km/h, Upstream speed=(30-3)=27 km/h
Hence, time required for 44 km downstream and 54 km upstream = (44/33) + (54/27) hrs = 10/3 hrs = 3 hrs 20 min.
Correct Option 8)
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