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  • A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Answers (1)

Solution:
Let speed of boat in still water = x km/h
Let speed of stream = y km/h
Speed of boat in upstream = (x - y) km/h
Speed of boat in downstream = (x + y) km/h
We know that time =\frac{distance}{speed}

So, \frac{30}{\left ( x-y \right )}+\frac{28}{x+y}= 7… (1)

\frac{21}{\left ( x-y \right )}+\frac{21}{x+y}= 5 … (2)

Put \frac{1}{\left ( x-y \right )}= u,\frac{1}{\left ( x+y \right )}= v in (1), (2)

30u + 28v = 7 … (3)
21u + 21v = 5 … (4)
Solve equation (3), (4)
Multiply equation (3) by 21 and (4) by 30
630u + 588 v = 147
630u + 630v = 150
_-______-____-________
+42v = +3

v= \frac{3}{42}= \frac{1}{14}

Put v= \frac{1}{14} in eq. (4)

21u+21\left ( \frac{1}{14} \right )= 5

21u= 5-\frac{3}{2}

21u= \frac{10-3}{2}

21u = \frac{7}{2}
u= \frac{7}{2\times 21}\Rightarrow u= \frac{1}{6}
We put u= \frac{1}{x-y}\, and\, v= \frac{1}{x+y}

So,

\frac{1}{x-y}= \frac{1}{6}            |           \frac{1}{x+y}= \frac{1}{14}
x-y=6..(5)                          x+y=14...(6)

By adding equation (5) and (6)
2x = 20
x = 10
Put x = 10 in eq. (6)
10 + y = 14
y = 4
Hence speed of the boat in still water = 10 km/hr.
Speed of the stream = 4 km/hr.

 

 

Posted by

infoexpert27

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