Question

What is the time it takes for two cyclists traveling at 25 km/h and 18 km/h to meet if they start 240 km apart?

Answer 1

To find out the time it takes for the two cyclists to meet, we first need to determine their combined speed. Since they are traveling towards each other, we can add their speeds together.

1. **Identifying the speeds of the cyclists:**
- Speed of the first cyclist: \( 25 \) km/h
- Speed of the second cyclist: \( 18 \) km/h

2. **Calculating the combined speed:**
\[
\text{Combined speed} = 25 \, \text{km/h} + 18 \, \text{km/h} = 43 \, \text{km/h}
\]

3. **Using the distance formula to calculate the time:**
We know that distance = speed × time. Rearranging this gives us time = distance / speed.

4. **Calculating the time taken to meet:**
Given the distance is \( 240 \) km and the combined speed is \( 43 \) km/h, the time taken to meet is:
\[
\text{Time} = \frac{240 \, \text{km}}{43 \, \text{km/h}}
\]

5. **Performing the division:**
\[
\text{Time} \approx 5.5814 \, \text{hours}
\]

To express this in hours and minutes:
- The decimal part \( 0.5814 \) hours can be converted to minutes by multiplying by \( 60 \):
\[
0.5814 \times 60 \approx 34.884 \, \text{minutes} \approx 35 \, \text{minutes}
\]

6. **Final answer:**
Therefore, the time it takes for the two cyclists to meet is approximately:
\[
\text{5 hours and 35 minutes}
\]