Two mechanics worked on a car. The first mechanic worked for $$ 5 $$ hours and the second mechanic worked for $$ 15 $$ hours. The final bill for the work was $$ \$ 1250 $$ . What was the rate charged per hour by each mechanic if their combined rate (sum of the two rates) was $$ \$ 140 $$ per hour?

Question

Two mechanics worked on a car. The first mechanic worked for $$ 5 $$ hours and the second mechanic worked for $$ 15 $$ hours. The final bill for the work was $$ \$ 1250 $$ . What was the rate charged per hour by each mechanic if their combined rate (sum of the two rates) was $$ \$ 140 $$ per hour?

Graham Wyatt · Accepted Answer

letrate for one car = xrate for second car = yso,$$\left [ \begin{array} { c } { x + y = 140 } \ { 5 x + 15 y = 1250 } \end{array} ight ] $$Isolate $$ x $$ for $$ x + y = 140 : \quad x = 140 - y$$ Substitute $$ x = 140 - y $$ $$ [ 5 ( 140 - y ) + 15 y = 1250 ] $$ Simplify $$ [ 700 + 10 y = 1250 ] $$ Isolate $$ y $$ for $$ 700 + 10 y = 1250 : \quad y = 55$$ For $$ x = 140 - y $$ Substitute $$ y = 55 $$ $$ x = 140 - 55$$ Simplify $$ x = 85$$ rate for one car = 85 per hour rate for second car = 55 per hour

Two mechanics worked on a car. The first mechanic worked for \( 5 \) hours and the second mechanic worked for \( 15 \) hours. The final bill for the work was \( \$ 1250 \) . What was the rate charged per hour by each mechanic if their combined rate (sum of the two rates) was \( \$ 140 \) per hour?

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Two mechanics worked on a car. The first mechanic worked for \( 5 \) hours and the second mechanic worked for \( 15 \) hours. The final bill for the work was \( \$ 1250 \) . What was the rate charged per hour by each mechanic if their combined rate (sum of the two rates) was \( \$ 140 \) per hour?

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