Question

A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Given:-

• Speed of motor boat in still water = 18km/h
• total distance = 24km

To find:-

• speed of this boat

Supposition:-

• let it's normal speed be x km/h

speed while going upstream = (18-x) km/h

speed while going down stream = (18+x) km/h

we know that,

• speed = $\sf\dfrac{distance}{time}$

• time = $\sf\dfrac{distance}{speed}$

According to the question:-

:$\implies$ $\sf\dfrac{24}{18-x} = \dfrac{24}{18+x} + 1$

:$\implies$ $\sf\dfrac{24}{18-x}-\dfrac{24}{18+x} = 1$

:$\implies$ $\sf \dfrac{24(18+x)-[24(18-x)]}{(18-x)(18+x)} = 1$

:$\implies$ $\sf\dfrac{432+24x-432+24x}{324-x²} = 1$

:$\implies$ $\sf 48x = 324-x²$

:$\implies$ $\sf x²+48x-324 = 0$

:$\implies$ $\sf x²+(54-6)x-324=0$

:$\implies$ $\sf x²+54x-6x-324 = 0$

:$\implies$ $\sf x (x+54)-6(x+54) = 0$

:$\implies$ $\sf (x-6)(x+54)$

:$\implies$ $\sf x = +6 , x = -54$

since, speed cannot be -ve .. 6km/h is right answer

Answer 2

Step-by-step explanation:

Refer to attachment!!

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