Question

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged $1650. What was the rate charged per hour by each mechanic if the sum of the two rates was $140 per hour?

Answer 1

x = rate of mechanic who worked 5 hours
y = rate of mechanic who worked 15 hours

Then

x + y = 235
5x + 15y = 2375

Just solve these 2 equations above for x and y.

x + y = 235 ⇒ x = 235 - y

Substitute into second equation to find y.

5(235 - y) + 15y = 2375

1175 - 5y + 15y = 2375

10y = 1200

y = 1200/10 = 120

x = 235 - y = 235 - 120 = 115

The mechanic who worked 5 hours charged $115 per hour, the one who worked 15 hours charged $120 per hour.