Question

Mark’s Pool Repair charges $50 for a service call, plus $40/h for labour. Jennifer’s Pools and Spas charges $30 for a service call, plus $45/h for labour. Find the length of a service call for which both companies charge the same amount.
Let x be the time to complete the work
Let y be the total cost of the work

Answer 1

Multiply each hourly rate by x ( time to complete the work) add it to the service call for each and then set the equations equal:

50 + 40x = 30 +45x

Subtract 30 from both sides:

20 + 40x = 45x

Subtract 40x from both sides:

20 = 5x

Divide both sides by 5

x = 4

The length is 4 hours.