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  • A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.    

A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.

 

 
 
 
 
 

Answers (1)

Lets assume 

Speed of boat = x

Speed of stream = y

So,

Upstream speed = x-y

Downstream speed = x+y

According to the question,

\frac{44}{x+y}+\frac{30}{x-y}=10 .....(1)

\frac{40}{x-y}+\frac{55}{x+y}=13 ... (2)

Multiplying eqn(2) with 3/4

\frac{30}{x-y}+\frac{165}{4(x+y)}=\frac{39}{4}

Subtractiong eqn(3) from eqn(1)

\frac{\left [ 44-\frac{165}{4} \right ]}{\left ( x+y \right )}=10-\frac{39}{4}

x+y=11 ....(4)

Subtracting the value of eqn(4) in eqn(1)

\frac{44}{11}+\frac{30}{x-y}=10

x-y=5.......(5)

Solving eqn (4) and eqn (5)

x = 8kmph and y = 3kmph.

Posted by

Safeer PP

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