To solve the problem of finding out how long it will take the boat to travel 100 kilometers, let's go through the calculations step-by-step:
1. Determine the rate of travel of the boat:
- The boat travels 48 kilometers in 3 hours.
- To find out how many kilometers the boat travels per hour (its rate of travel), we divide the distance traveled by the time taken:
[tex]\[
\text{Rate of Travel} = \frac{\text{Distance Travelled}}{\text{Time Taken}} = \frac{48 \text{ km}}{3 \text{ hours}} = 16 \text{ km/hour}
\][/tex]
2. Calculate the time to travel 100 kilometers at the same rate:
- Now that we know the boat travels at a rate of 16 kilometers per hour, we need to find out how long it takes to travel 100 kilometers.
- To do this, we divide the desired distance by the rate of travel:
[tex]\[
\text{Time to Travel 100 km} = \frac{\text{Desired Distance}}{\text{Rate of Travel}} = \frac{100 \text{ km}}{16 \text{ km/hour}} = 6.25 \text{ hours}
\][/tex]
Based on this step-by-step solution, the boat will take 6.25 hours to travel 100 kilometers. Therefore, the correct answer is:
\- 6.25 hours
