Solution: Downstream Swim Time Calculation

This section details the calculation for the time taken to swim downstream, using the provided speeds and distance.

Given Information

• Speed of stream ($v_s$) = 3 km/h
• Speed of man in still water ($v_m$) = 6 km/h
• Distance downstream ($d$) = 37 km

Calculating Downstream Speed

To find the speed while swimming downstream, we add the speed of the man in still water to the speed of the stream.

Downstream speed ($v_d$) is calculated as: $v_d = v_m + v_s$

Substituting the given values: $v_d = 6 \text{ km/h} + 3 \text{ km/h} = 9 \text{ km/h}$

Calculating Time Taken

The time taken to travel a certain distance is found by dividing the distance by the speed.

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

Using the downstream speed and distance:

Time $= \frac{d}{v_d} = \frac{37 \text{ km}}{9 \text{ km/h}}$

Time $= \frac{37}{9}$ hours

Converting to Mixed Fraction

To express the time as a mixed fraction:

Divide 37 by 9: $37 \div 9 = 4$ with a remainder of $1$.

So, the time is $4 \frac{1}{9}$ hours.

Final Result

The time taken by the man to swim 37 km downstream is $4 \frac{1}{9}$ hours.