Trains Boats and Streams Practice Test 4 with solutions

Question : 31 of 40

Marks: +1, -0

A swimmer can go 10 km upstream and come back to the starting point in 55 minutes. Find the time taken by the swimmer to go and come back 15 km in the still water if the rate of current is 2 km/hour.

1.375 hour
2 hour
2.25 hour
1.142 hour
2.02 hour

Validate

Solution:

Let the speed of the boat = x km/hour
=

{10}/{x-2}+{10}/{x+2}

{55}/{60}

{x+2+x-2}/{x^2-4}

{11}/{120}

240x = 11x2 - 44

11x^2

- 240x - 44 = 0

11x^2

- 242x + 2x - 44 = 0
(x - 22) (11x + 2) = 0
x = 22 km/hour
Rate downstream = 24 km/hour
Rate upstream = 20 km/hour
Time taken =

{15}/{24}+{15}/{20}

= 0.625 + 0.75
= 1.375 hour

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