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Skylar is a lifeguard at a swimming pool. Last week, they worked
3(3)/(4) equal-length shifts, because rain closed the pool early one day. Those shifts totaled
11(1)/(4) hours of work.
How long is a single shift? hours

Skylar is a lifeguard at a swimming pool. Last week, they worked $3 \frac{3}{4}$ equal-length shifts, because rain closed the pool early one day. Those shifts totaled $11 \frac{1}{4}$ hours of work. $\newline$ How long is a single shift? $\newline$ hours

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Interpret parts of quadratic expressions: word problems

Full solution

Q. Skylar is a lifeguard at a swimming pool. Last week, they worked

3 \frac{3}{4}

equal-length shifts, because rain closed the pool early one day. Those shifts totaled

11 \frac{1}{4}

hours of work.

\newline

How long is a single shift?

\newline

hours

Understand the problem: Understand the problem. $\newline$ Skylar worked $3\left(\frac{3}{4}\right)$ shifts which totaled $11\left(\frac{1}{4}\right)$ hours. We need to find the length of a single shift.
Convert to improper fractions: Convert mixed numbers to improper fractions to make calculations easier. $\newline$ $3\left(\frac{3}{4}\right)$ shifts can be converted to $\left(3\times 4 + 3\right)/4 = \left(12 + 3\right)/4 = \frac{15}{4}$ shifts. $\newline$ $11\left(\frac{1}{4}\right)$ hours can be converted to $\left(11\times 4 + 1\right)/4 = \left(44 + 1\right)/4 = \frac{45}{4}$ hours.
Calculate single shift length: Calculate the length of a single shift. $\newline$ To find the length of a single shift, divide the total hours worked by the number of shifts. $\newline$ $(45/4)$ hours $\div$ $(15/4)$ shifts = $(45/4) \times (4/15)$ = $45/15$ = $3$ hours.

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