Question

Mathew drives m miles in X hours. How many hours would he save if he drove the same distance k miles per hour?

Answer 1

To calculate the time Mathew would save by driving at a speed of \( k \) miles per hour instead of \( \frac{m}{X} \) miles per hour, we can follow these steps:

1. **Determine Mathew's original speed:**
- Mathew drives \( m \) miles in \( X \) hours, so his speed is:
\[
\text{original speed} = \frac{m}{X} \text{ miles per hour}
\]

2. **Calculate the time taken at the original speed:**
- The time taken to drive \( m \) miles at his original speed is \( X \) hours (as given).

3. **Calculate the time taken at the new speed \( k \) miles per hour:**
- To find the time taken to drive \( m \) miles at the speed \( k \) miles per hour, we use the formula:
\[
\text{time at } k = \frac{m}{k} \text{ hours}
\]

4. **Calculate the time saved:**
- The time saved by switching from the original speed to speed \( k \) is:
\[
\text{time saved} = \text{original time} - \text{new time}
\]
- Plugging in the expressions for the original and new times, we get:
\[
\text{time saved} = X - \frac{m}{k}
\]

Thus, the number of hours Mathew would save if he drove the same distance at \( k \) miles per hour is:
\[
\text{time saved} = X - \frac{m}{k}
\]