Question

QuestionTutorials3 – Work, Rate, and Time in a System of EquationsLEARNING OBJECTIVE: Solve a work, rate, and time, problem by using a system of equations.Timothy has hired Cynthia and Dominic to cover the roof with shingles. Dominic can install 180 shinglesin the same time it takes Cynthia to install 150 shingles, which can be shown using the followingrelationship where d and c are the respective rates for Dominic and Cynthia:180/d=150/cAlso, Dominic can install 10 shingles more per hour than Cynthia.

Answer 1

Cynthia can install 50 shingles per hour

Here, we want to get the number of shingles Cynthia can install per hour

From the question, we have it that for the same one hour, Timothy install more shingles

Let the rate taken for Cynthia be x shingles per hour

Since Timothy installs 10 more, then the rate for Timothy will be (10 + x) shingles per hour

Since their hourly rate is equal, we have it that;

`\begin{gathered} (150)/(x)\text{ = }(180)/(x+10) \\ 150(x+10)\text{ = 180x} \\ 150x\text{ + 1500 = 180x} \\ 180x-150x\text{ = 1500} \\ 30x\text{ = 1500} \\ \text{ x = }(1500)/(30) \\ x\text{ = 50} \end{gathered}`

What this mean is that Cynthia fixes 50 shingles per hour