Question

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

Answer 1

$\Huge{\underline{\underline{\mathfrak{ Solution \colon }}}}$

Given, The speed of boat in still water =18 km /hr

Let the speed of stream be x km/ hr

Speed of the boat uperstream= speed of boat in a still water - speed of the stream.

Therefore, Speed of the boat upstream

Therefore, Speed of the boat upstream = ( 18 - x ) km/ hr

Speed of the boat downstream = speed of a boat in a still water + speed of the stream

Therefore,Speed of boat downstream

= ( 18 + x ) km/ hr

Time of upstream journey - Time for downward stream journey +1 hr

$\frac{ \:\text{distance covered upstream}}{ \:\text{speed of the boat stream}}$

$= \frac{ \:\text{distance covered downstream}}{ \:\text{speed of the boat stream}} + 1 \text{hr}$

$⟹ \frac{24}{18 - \text{ x} } - \frac{24}{18 - \text{x}} = 1$

$⟹ \frac{24 \text{km}}{(18 - \text{x \: per hr)}} = \frac{24 \text{km}}{ (18 + \text{x} )\text{ \: km \: per \: hr}} = 1$

$= > \frac{432 + 24 \text{x} - 432 + 24 \text{x}}{(18 - \text{x})(18 + \text{x}} = 1$

$⟹48 \text{x} = 324 - { \text{x}}^{2}$

$⟹ { \text{x}}^{2} + 48 \text{x} - 324 = 0$

$⟹ { \text{x}}^{2} + 54 \text{x} - 6 \text{x} - 324 = 0$

$⟹ \text{x}( \text{x} + 54)( \text{x} + 54) = 0$

$⟹ \text{x} + 54 = 0 \: or \: x - 6 = 0$

$⟹ \text{x} = - 54 \: or \: x = 6$

Thus the speed of stream is 6km/ hr.

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Answer 2

Answer:

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr

Hope It helps you dear mate