Understanding Boat and Current Problems

This problem involves calculating the distance a boat travels downstream. To solve this, we need to understand how the speed of the boat in still water and the speed of the current combine when the boat moves downstream (in the same direction as the current).

Key Information Provided

• Speed of the boat in still water ($v_b$): 15 km/h
• Speed of the current ($v_c$): 9 km/h
• Time of travel ($t$): 25 minutes
• Direction of travel: Downstream

Calculating Downstream Speed

When a boat travels downstream, the speed of the current adds to the speed of the boat in still water. This is because the current helps push the boat forward.

The formula for downstream speed ($v_{down}$) is:

$$ v_{down} = v_b + v_c $$

Plugging in the given values:

$$ v_{down} = 15 \text{ km/h} + 9 \text{ km/h} = 24 \text{ km/h} $$

So, the effective speed of the boat when moving downstream is 24 km/h.

Converting Time to Hours

The time is given in minutes, but the speed is in kilometers per hour. We need to convert the time to hours to maintain consistent units for calculation.

Time ($t$) = 25 minutes

To convert minutes to hours, divide by 60:

$$ t = \frac{25}{60} \text{ hours} $$

Simplifying the fraction:

$$ t = \frac{5}{12} \text{ hours} $$

Calculating the Distance Traveled Downstream

The relationship between distance, speed, and time is given by the formula:

$$ \text{Distance} = \text{Speed} \times \text{Time} $$

In this case, the distance ($d$) traveled downstream is:

$$ d = v_{down} \times t $$

Using the calculated downstream speed and the converted time:

$$ d = 24 \text{ km/h} \times \frac{5}{12} \text{ hours} $$

$$ d = \frac{24 \times 5}{12} \text{ km} $$

$$ d = 2 \times 5 \text{ km} $$

$$ d = 10 \text{ km} $$

Final Answer

The distance travelled by the boat downstream in 25 minutes is 10 km.