a boat travel at a speed of 20 km/h in still water the current in a river flows at 5 km/h    so that downstream the boat can travel at 25 km/h and upstream it travels at only 15 km/h the boat has only enough fuel for 3 hours.after what time does the boat turn around so that it has enough fuel to return to base

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Let us say boat travel xkm distance from base in t1 hours down stream when it turn around and comes upstream.

`t1 = x/25`

For the return travel let us say it takes t2 hours.

`t2 = x/15`

How ever at the critical time limit;

`t1+t2 = 3`

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Let us say boat travel xkm distance from base in t1 hours down stream when it turn around and comes upstream.

`t1 = x/25`

 

For the return travel let us say it takes t2 hours.

`t2 = x/15`

 

How ever at the critical time limit;

`t1+t2 = 3`

`x/25+x/15 = 3`

`(x(3+5))/75 = 3`

       `x = (75xx3)/8`

        `x = 28.125`

 

`t1 = x/25 = 28.125/25 = 1.125`

 

So the boat should turn around in 1.125 hours to return to base without running out of fuel.

 

 

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