I don't understand how to find the equation to solve this.
A family drove two cars to a reunion. The first car traveled at 50 mph. The second car left 1 hour later and traveled at 65 mph. How long will it take for the second car to catch up to the first car?
the second car is going 15 mph faster than the first
when the 2nd cars starts out, the 1st car has gone 50 miles already.
So, how long does it take to make up 50 miles, going a relative speed of 15 mi/hr?
To solve this problem, you need to find the time it takes for the second car to catch up to the first car. Let's break the problem down step by step:
Step 1: Define the variables:
Let's denote:
- t as the time the second car takes to catch up to the first car,
- d as the distance traveled by the first car when the second car catches up.
Step 2: Understand the problem:
The first car starts 1 hour earlier than the second car, so it has already traveled for an hour when the second car starts. The distance traveled by the first car during that time is given by the equation d = 50 * 1 = 50.
Step 3: Create an equation for the second car:
The second car is traveling at 65 mph, and it started 1 hour later than the first car. So, the distance traveled by the second car is given by the equation d = 65 * t.
Step 4: Set up the equation:
Since both cars travel the same distance when the second car catches up to the first car, we can equate the two equations: 50 = 65 * t.
Step 5: Solve for t:
To find t, divide both sides of the equation by 65:
50 / 65 = t.
Using a calculator, you can determine that 50 divided by 65 is approximately 0.7692.
Step 6: Interpret the answer:
The equation tells us that it will take approximately 0.7692 hours for the second car to catch up to the first car. Since time is usually expressed in hours and minutes, you can convert the decimal into minutes and seconds if needed.
Therefore, it will take about 46 minutes and 9 seconds for the second car to catch up with the first car.