Question

Please solve the above question with attachment​

Answer 1

Answer:

$\blue\large\boxed{\star \: \: The\:Speed\:of\:Stream\:is\:\frac{5\sqrt{6} }{2}\:km/hour \:\:\star}$

Step-by-step explanation:

✩Given:-

• Speed of boat in still water =15 km/hr.
• It can go 30 km upstream and return downstream to the original point in 7 hours and 12 minutes.

✩To Find:-

  Speed of the Stream.

✩Solution:-

Let the speed of the Stream be x km/hour.

Downstream speed = (15 + x) km/hour

Upstream speed = (15 - x) km/hour

→Time taken to go 30 km upstream=$\frac{30}{15-x}\:hours$

→Time taken to go 30 km upstream=$\frac{30}{15+x}\:hours$

Now, According to the Question:-

$\implies\frac{30}{15+x}+\frac{30}{15-x}=7+\frac{12}{60}$

$\implies 30(\frac{1}{15+x}+\frac{1}{15-x})=7+\frac{1}{5}$

Taking LCM on Both Sides:-

$\implies 30(\frac{15+x+15-x}{(15+x)(15-x)})=\frac{35+1}{5}$

$\implies 30(\frac{15+15}{(15)^2-(x)^2})=\frac{36}{5}$

$\implies 15(\frac{30}{225-x^2})=\frac{12}{5}$

$\implies 5(\frac{30}{225-x^2})=\frac{4}{5}$

$\implies \frac{150}{225-x^2}=\frac{4}{5}$

Cross Multiplying Both sides:-

$\implies 5\times(150)=4\times(225-x^2)$

$\implies 750=900-4x^2$

$\implies 4x^2=900-750$

$\implies 4x^2=150$

$\implies x^2=\frac{150}{4}$

$\implies x=\sqrt{\frac{150}{4}}$

$\implies x=\frac{5\sqrt{6} }{2}\:km/hour$

$\boxed{\therefore\:The\:Speed\:of\:Stream\:is\:\frac{5\sqrt{6} }{2}\:km/hour}$