A boat travels 2km upstream and 2km downstream. The total time of the trip is 1 hour. The speed of the stream is 2km/h. What is the speed of the boat in still water?

2 = ( v + 2 ) × t1 ;

2 = ( v - 2 ) × t2 ;

t1 + t2 = 1 ;

where v is the speed of the boat in still water ; t1 is the time upstream ; t2 is the tome downstream ;

Then, v + 2 = 2 / t1 and v - 2 = 2 / t2 ;

v = 2 / t1 - 2 and v = 2 / t2 + 2 ;

2 / t1 - 2 = 2 / t2 + 2 ;

2 / t1 - 2 / t2 = 4 ;

1 / t1 - 1 / t2 = 2 ;

t2 - t1 = 2t1t2 ;

But, t2 = 1 - t1 ;

1 - t1 - t1 = 2t1( 1 - t1 ) ;

1 - 2t1 = 2t1 - 2t1^2 ;

2t1^2 - 4t1 + 1 = 0 ; quadratic equation ;

solving this equation,

t1 ≈ 0.29 hour ;

v ≈ 2 / 0.29 - 2;

v ≈ 4.89 km/h ;

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