ellamarsh34
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Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?

Respuesta :

y = 5x + 3
y = 5.5x + 2
0.5x = 1
x = 2
y = 13
I hope any of this will help you. c:

The equation that could be used to solve the number of hours Ben ran during each half of the race will be y = 5x + 3 and y = 5.5x + 2

During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. Therefore, the number of miles covered will be:

y = 5x + 3

During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. Therefore, the number of miles covered will be:

y = 5.5x + 2

Then using both equations will be:

y = 5x + 3

y = 5.5x + 2

Subtract the equations

0.5x = 1

x = 1/0.5 = 2

Therefore, the value of y will be:

y = 5x + 3 = 5(2) + 3 = 13

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