A motorboat, 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:

To find the speed of the stream, we can break down the problem into parts. Let's denote the speed of the stream as s km/hr. The speed of the motorboat in still water is 15 km/hr.

Calculating Effective Speeds

When the boat is going downstream, its effective speed is:

• Downstream speed = 15 + s

When the boat is going upstream, its effective speed is:

• Upstream speed = 15 - s

Time Taken for Each Journey

The distance traveled downstream is 30 km, and the time taken can be calculated as:

• Time downstream = Distance / Speed = 30 / (15 + s)

For the return journey upstream, the time taken is:

• Time upstream = Distance / Speed = 30 / (15 - s)

Total Time Calculation

The total time for both journeys is given as 4 hours and 30 minutes, which is equal to 4.5 hours. Therefore, we can set up the equation:

30 / (15 + s) + 30 / (15 - s) = 4.5

Solving the Equation

To solve for s, we first find a common denominator:

• Common denominator = (15 + s)(15 - s)

Rearranging the equation gives:

30(15 - s) + 30(15 + s) = 4.5(15 + s)(15 - s)

Expanding and simplifying leads to:

• 450 - 30s + 450 + 30s = 4.5(225 - s²)
• 900 = 1012.5 - 4.5s²

Rearranging further results in:

• 4.5s² = 112.5
• s² = 25
• s = 5

Final Result

The speed of the stream is 5 km/hr.