Question

two mechanics worked on a car the first mechanic charge 115 per hour and the charge 110 per hour the mechanic work for a combined total of 15 hours and then together they charge a total of 1700 How long did each mechanic work

Answer 1

We know that the total cost is $1700 and the total work hours are 15.

We will call x the number of hours worked by the first mechanic and y the number of worked hours by the second mechanic.

The total work hours is the sum of x and y and equal to 15:

`x+y=15`

The cost of each mechanic is the price per hour multiplied by the work hours, so we can write:

`115\cdot x+110\cdot y=1700`

We have a system of linear equations.

We will solve it by substitution.

`x+y=15\longrightarrow y=15-x`
`\begin{gathered} 115x+110y=1700 \\ 115x+110(15-x)=1700 \\ 115x+1650-110x=1700 \\ 115x-110x=1700-1650 \\ 5x=50 \\ x=(50)/(5) \\ x=10 \end{gathered}`
`y=15-x=15-10=5`

Answer: the first mechanic worked 10 hours and the second mechanic worked 5 hours.