Calculating Downstream Travel Time

To find the time taken to swim downstream, we first need to determine the downstream speed. The downstream speed is the sum of the man's speed in still water and the speed of the stream.

Downstream Speed Calculation

Given:

• Speed of stream = 3 km/h
• Speed of man in still water = 5 km/h

The formula for downstream speed is:

$ \text{Speed}_{\text{downstream}} = \text{Speed}_{\text{man}} + \text{Speed}_{\text{stream}} $

Substituting the given values:

$ \text{Speed}_{\text{downstream}} = 5 \text{ km/h} + 3 \text{ km/h} = 8 \text{ km/h} $

Time Calculation for Downstream Swim

The time taken to cover a distance is calculated using the formula:

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

Given:

• Distance = 26 km
• Downstream Speed = 8 km/h

Calculating the time:

$ \text{Time}_{\text{downstream}} = \frac{26 \text{ km}}{8 \text{ km/h}} $

Simplify the fraction:

$ \text{Time}_{\text{downstream}} = \frac{13}{4} \text{ hours} $

Converting Time to Mixed Fraction

To express the time in hours and minutes, convert the improper fraction to a mixed number:

$ \frac{13}{4} \text{ hours} = 3 \frac{1}{4} \text{ hours} $

Therefore, the time taken by the man to swim 26 km downstream is $3\frac{1}{4}$ hours.