Question

Two cars leave New York at the same time traveling in opposite directionsOne travels at an average speed of 71 mph and the other at 72 mphin how many hours will they be 572 miles apart? Let x = time of travel for the first car and y = time of travel for the second carThen the system that models the problem is x = y; 71x + 72y = 572 Solve the system by using the method of addition

Answer 1

To solve the system using the method of addition, multiply the first equation by 72 and the second equation by 71 to make the coefficients of x in both equations the same. Subtract the first equation from the second equation to eliminate y. Solve the resulting equation to find the value of x. Substitute the value of x back into the first equation to find y. The cars will be 572 miles apart in 4 hours.

Step-by-step explanation:

To solve the system using the method of addition, we need to eliminate one variable. In this case, we can eliminate y. Let's multiply the first equation by 72 and the second equation by 71 to make the coefficients of x in both equations the same.

Multiplying the first equation by 72: 72(x = y)

72x = 72y

Multiplying the second equation by 71: 71(71x + 72y = 572)

5041x + 5136y = 40732

Now, subtract the first equation from the second equation:

5041x + 5136y - 72x = 40732 - 72y

4969x + 5064y = 40660

Now we have a single equation with only x as the variable. Solve this equation to find the value of x:

4969x = 40660 - 5064y

x = (40660 - 5136y) / 4969

Now, substitute the value of x back into the first equation to find y:

x = y

(40660 - 5136y) / 4969 = y

Now we have a quadratic equation. Simplify and solve for y:

40660 - 5136y = 4969y

10105y = 40660

y = 4

Now substitute the value of y back into the first equation to find x:

x = y

x = 4

Therefore, they will be 572 miles apart in 4 hours.