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A boat goes 7 km upstream in 2 hours and same distance downstream in 40 minutes. How long will it take to go \(17\frac{1}{2}km\) in still water ?
1. 2.5 hours
2. 2 hours
3. 2.2 hours
4. 3 hours

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Correct Answer - Option 1 : 2.5 hours

Given:

A boat goes 7 km upstream in 2 hours and same distance downstream in 40 minutes

Concept used:

Boat and Stream.

Calculation:

Let the speed in still water be x km/hr

Speed of Stream be y km/hr

Speed Downstream = (x + y) km/hr

Speed Upstream = (x - y) km/hr

Boat covers 7 km upstream in 2 hours 

x - y = 7/2  

Boat covers 7 km downstream in 40 minutes

x + y = \(\frac{{7 \times 3}}{2} = \frac{{21}}{2}km/hr\)

Equation 1 = 2x - 2y = 7

Equation 2 = 2x + 2y = 21

Solving both equations we get

x = 7 km/hr

Time required to travel \(17\frac{1}{2}km\)

Time = \(\frac{{35}}{{2 \times 7}} = \frac{5}{2}\)

Time taken = 2.5 hours

 

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