Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h.
How far must the faster car travel before it has a 15-min lead on the slower car?

To solve this problem, we need to determine how far the faster car must travel before it has a 15-minute (or 1/4 hour) lead on the slower car.

### Step-by-step solution:

1. **Define the variables:**
   - Speed of the slower car: \( v_1 = 55 \, \text{mi/h} \)
   - Speed of the faster car: \( v_2 = 70 \, \text{mi/h} \)
   - Time difference between the two cars: \( t = 15 \, \text{minutes} = \frac{1}{4} \, \text{hour} \)

2. **Relative speed:**
   The faster car gains on the slower car at a relative speed of:
   \[
   v_{\text{relative}} = v_2 - v_1 = 70 - 55 = 15 \, \text{mi/h}
   \]

3. **Distance lead:**
   The distance the faster car must travel to have a 15-minute (or \( \frac{1}{4} \) hour) lead is the distance the slower car travels in that time, which is:
   \[
   \text{Distance} = v_{\text{relative}} \times t = 15 \times \frac{1}{4} = 3.75 \, \text{miles}
   \]

### Conclusion:
The faster car must travel **3.75 miles** before it has a 15-minute lead on the slower car.

Do you want more details, or have any questions?

Here are 5 related questions:
1. What if the faster car was traveling at 80 mi/h?
2. How long would it take for the faster car to gain a 30-minute lead?
3. If both cars start at the same time, how long will it take the faster car to gain a 5-mile lead?
4. What if the slower car's speed was 60 mi/h instead of 55 mi/h?
5. How far would both cars travel in 2 hours?

**Tip:** Converting time to hours when working with speeds in miles per hour ensures consistency in your calculations!

Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h. How far must the faster car travel before it has a 15-min lead on the slower car?

Learn how to calculate the distance a faster car must travel to gain a 15-minute lead on a slower car. This problem involves calculating relative speed and applying basic distance and time formulas. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation