Question

A boat whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

Answer 1

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Here is the solution:

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Speed of the boat in still water = 15 km/h

Distance (one way) = 30 km

Let the speed of the stream be x km/h

Downstream:

Speed = (15 + x) km/h

time = Distance ÷ Speed

Time = 30 / (15 + x)

Upstream:

Speed = (15 - x) km/h

Time = Distance ÷ Speed

Time = 30 / (15 - x)

The total time taken is 4 hours 30 mins

⇒ 4 hours 30 mins = 4.5 hour

Form equation and solve for x:

$\dfrac{30}{15 + x} + \dfrac{30}{15 - x}= 4.5$

Put into single fraction:

$\dfrac{30(15 - x) + 30(15 + x)}{(15 + x)(15 - x)}= 4.5$

Cross Multiply:

$30(15 - x) + 30(15 + x) = 4.5(15 + x)(15 - x)$

Take out common factor 15 on LHS and apply (a + b)(a - b) = a² - b²) on RHS:

$30(15 - x + 15 + x) = 4.5(15^2 - x^2)$

Common like terms:

$30(30) = 4.5(225 - x^2)$

Simplify LHS:

$900= 4.5(225 - x^2)$

Divide both sides by 4.5:

$200 = 225 - x^2$

Subtract 225 from both sides:

$-25= - x^2$

Switch side and divide both sides by -1:

$x^2 = 25$

Square root both sides:

$x = 5$

Answer: The speed of the stream is 5 km/h

Answer 2

A boat's speed is 15 km/h in still water.

The speed of the stream (in km/hr) be x.

Distance between the opposite banks = 30 km

Speed of boat (upstream)= 15-x km/hr

Speed of boat (downstream)= 15+x km/hr

We know that ,

Distance/speed = time

Given ,

30/15-x + 30/15+x = 4+1/2 hrs

Solve the above equation and find the value of x.

Ans. x= 5 km/h