Question

Two cars drive from Miami to Atlanta. The first car drives 75miles per hour. The second car leaves four hours later and drives 90 miles per hour. Write and solve an equation to determine after how much time the two cars be the same distance from Miami. Round to the nearest hour.

Please show work:)

Answer 1

two cars will be the same distance from Miami after 24 hours.

Explanation:

| Car | Rate | Time | Distance |

| First | 75 mph | t hours | 75t miles |

| Second | 90 mph | (t-4) hours | 90(t-4) miles |

We want to find the time t when the two cars are the same distance from Miami. This means that their distances are equal, so we can set up an equation by equating the distance expressions:

75t = 90(t-4)

To solve for t, we need to simplify and isolate it on one side of the equation. We can do this by following these steps:

- Expand the parentheses on the right side by multiplying 90 with t and -4.

- Subtract 90t from both sides to eliminate it on the right side.

- Add 360 to both sides to eliminate it on the left side.

- Divide both sides by -15 to get t alone.

The equation will look like this after each step:

- 75t = 90t - 360

- -15t = -360

- -15t + 360 = 0

- t = \frac{0}{-15} = 0

The solution is t = 24. This means that the two cars will be the same distance from Miami after 24 hours.

Answer 2

To determine when the two cars will be the same distance from Miami, we can set up an equation based on their respective speeds and times.

Let's assume t represents the time it takes for the second car to catch up to the first car. Since the first car left four hours earlier, it will have been driving for t + 4 hours when the second car catches up.

The equation for the distance traveled by the first car is given by:

Distance1 = Speed1 * Time1

Distance1 = 75 * (t + 4)

Similarly, the equation for the distance traveled by the second car is:

Distance2 = Speed2 * Time2

Distance2 = 90 * t

Since the two cars will be at the same distance from Miami when they meet, we can set these two distances equal to each other:

75 * (t + 4) = 90 * t

Now, let's solve this equation to find the value of t:

75t + 300 = 90t

300 = 90t - 75t

300 = 15t

t = 300 / 15

t = 20

Therefore, after approximately 20 hours, the second car will catch up to the first car, and they will be at the same distance from Miami.