Understanding the Rowing Problem

This question asks us to find the time it takes for a man to travel a certain distance downstream. We are given his rowing speed in still water and the speed of the stream.

Key Information Provided:

• Speed of the man in still water: 10 km/h
• Speed of the stream: 7 km/h
• Distance to travel downstream: 85 km

Calculating Downstream Speed

When rowing downstream, the speed of the stream adds to the speed of the boat in still water. This combined speed is the effective speed at which the boat moves relative to the bank.

The formula for downstream speed is:

Speeddownstream = Speedstill water + Speedstream

Plugging in the given values:

Speeddownstream = 10 \text{ km/h} + 7 \text{ km/h} = 17 \text{ km/h}

Calculating the Time Taken

Now that we have the downstream speed and the distance, we can calculate the time taken using the basic formula relating distance, speed, and time.

The formula is:

Time = \frac{\text{Distance}}{\text{Speed}}

Using the distance and the calculated downstream speed:

Time = \frac{85 \text{ km}}{17 \text{ km/h}}

Time = 5 \text{ hours}

Conclusion

Therefore, the time taken for the man to row 85 km downstream is 5 hours.