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Problem 1173

# Two cars are traveling 40 and 50 miles per hour, respectively. If the second car starts out 5 miles behind the first car, how long will it take the second car to overtake the first car?

Expert verified
It will take the second car 0.5 hours or 30 minutes to overtake the first car.
See the step by step solution

## Step 1: Assign variables to the given information

Let's assign the variables to the given information: - Speed of the first car (V1) = 40 mph - Speed of the second car (V2) = 50 mph - Initial distance between the cars (D) = 5 miles We have to find the time (T) it takes the second car to overtake the first car.

## Step 2: Set up the equation using the distance formula

Since we know that distance = speed × time, we can set up an equation as follows: Distance covered by Car 1 = Distance covered by Car 2 - Initial distance between them V1 × T = (V2 × T) - D

## Step 3: Substitute the variables with the given values and solve for T

Now, let's substitute the given values into our equation and solve for T: $$40T = (50T) - 5$$

## Step 4: Rearrange the equation to isolate T and calculate the solution

First, we can move the term involving T from the right side to the left side of the equation to have T terms on one side of the equation: $$40T - 50T = -5$$ Now, combine the T terms: $$-10T = -5$$ Next, divide both sides of the equation by -10 to solve for T: $$T = \frac{-5}{-10}$$ Finally, calculate the value of T: $$T = 0.5$$

## Step 5: Interpret the solution

The time, T = 0.5 hours. Therefore, it will take the second car 0.5 hours or 30 minutes to overtake the first car.

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