Question

You are remodeling your kitchen. You've contacted two tiling companies who gladly told you how long it took their workers to tile a floor of a similar size. Jim completed half the floor in 7 hours. Pete completed the other half of the floor in 6 hours. If Pete can lay 15 more tiles per hour than Jim, what equation would you use to find the rate that Jim can lay tiles? Let x represent Jim's rate.
explain why the answer is correct

Answer 1

The answer is 7x = 6(x + 15)

x - Jim's rate
y - Pete's rate
Jim completed half the floor in 7 hours:  7x = half of the floor
Pete completed the other half of the floor in 6 hours:    6y = half of the floor
So: 7x = 6y

Pete can lay 15 more tiles per hour than Jim: y = x + 15

7x = 6y
y = x + 15

Substitute the second equation into the first one:
7x = 6(x + 15)