Question

solve the following word problem. two cars leave boston at the same time traveling in opposite directions. one travels at an average speed of 75 mph and the other at 63 mph. in how many hours will they be 276 miles apart? let x = time of travel for the first car and y = time of travel for the second car. then the system that models the problem is \\(\

$$\begin{cases} x = y \\\\ 75x + 63y = 276 \\end{cases}$$

\\). solve the system by using the method of addition. answer how to enter your answer (opens in new window) time of travel for the first car time of travel for the second car

Explanation:

Step1: Substitute \( x = y \) into the second equation

Since \( x = y \), we can replace \( x \) with \( y \) in the equation \( 75x + 63y = 276 \). So we get \( 75y + 63y = 276 \).

Step2: Combine like terms

Combine the terms with \( y \): \( (75 + 63)y = 276 \), which simplifies to \( 138y = 276 \).

Step3: Solve for \( y \)

Divide both sides of the equation \( 138y = 276 \) by 138: \( y=\frac{276}{138} = 2 \).

Step4: Solve for \( x \)

Since \( x = y \), then \( x = 2 \).

Answer:

time of travel for the first car: \( 2 \) hours
time of travel for the second car: \( 2 \) hours