Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1700 . What was the rate charged per hour by each mechanic if the sum of the two rates was $225 per hour?

Question

whpalmer4 · Answer

Let $m_1$ be the rate charged by the first mechanic, and $m_2$ be the rate charged by the second.  We know that together they charge $225/hour, so
$$m_1 + m_2 = 225$$

We know that the first mechanic worked 10 hours, and charged $10m_1$
We know the second mechanic worked 5 hours, and charged $5m_2$
Together, they charged $1700, or $$10m_1 + 5m_2 = 1700$$

Solve the system of two equations in two unknowns for the rates charged.