Question

umple 15: 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 stream he x km/h​

Answer 1

Let the speed of the stream be xkm/hr

While going upstream

Distance=24km

speed=speed of boat-speed of stream=18-x

$\rm time = \frac{distance}{speed} \\ \implies \rm \boxed{ t_{1} = \frac{24}{18 - x}} ...1$

While going downstream

Distance=24

Speed=18+x

$\rm time = \frac{distance}{speed} \\ \implies \rm \boxed { t_{1} = \frac{24}{18 + x}}$

ATQ

$\rm t_{1} = t_{2} + 1 \\ \rm t_{1} - t_{2} =1 \\ \implies \rm \frac{24}{18 - x} - \frac{24}{18 + x} = 1 \\ \implies \rm \frac{24(18 + x) - 24(18 - x)}{(18 - x)(18 + x)} = 1 \\ \rm \implies \frac{432 + 24x - 432 + 24x}{324 - {x}^{2} } = 1 \\ \rm \implies 48x = 324 - {x}^{2} \\ \rm \implies \boxed{ {x}^{2} - 48x - 324 = 0}$

Using quadratic formula

$\rm x = \frac{ - 48 \pm \sqrt{ {48 }^{2} + 1296} }{2} \\ \rm \implies x = \frac{ - 48 \pm \sqrt{3600} }{2} \\ \rm \implies x = \frac{ - 48 \pm 60}{2} \implies \boxed{x = 6 \: or \: x = - 54}$

Since speed of x is cannot be negative.So,we reject -54. Therefore,speed of the stream is 6km/hr

Answer 2

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