Answered

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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?

Sagot :

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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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