We know that Sammy ran $3 \frac{3}{5}$ miles in $33$ minutes. We want to determine his pace in miles per hour. We can do so in two steps.

Convert $33$ minutes into hours.
Calculate Sammy's pace.

We can do these steps one at a time.

Convert Minutes Into Hours

We want to rewrite

33

minutes into hours. We can do so using a conversion factor

\frac{1 hour}{6 0 minutes}

to move from minutes to hours.

33 minutes \cdot \frac{1 hour}{6 0 minutes}

Now let's simplify our expression.

33 minutes \cdot \frac{1 hour}{6 0 minutes}

MoveLeftFacToNum

$a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$

\frac{3 3 minutes \cdot 1 hour}{6 0 minutes}

CancelCommonFac

Cancel out common factors

\frac{3 3 minutes \cdot 1 hour}{6 0 minutes}

SimpQuot

Simplify quotient

\frac{3 3 \cdot 1 hour}{6 0}

▼

Simplify

MovePartNumRight

$\frac{a \cdot b}{c} = \frac{a}{c} \cdot b$

\frac{3 3 \cdot 1}{6 0} hour

IdPropMult

Identity Property of Multiplication

\frac{3 3}{6 0} hour

ReduceFrac

$\frac{a}{b} = \frac{a / 3}{b / 3}$

\frac{1 1}{2 0} hour

CalcQuot

Calculate quotient

0.55 hour

Sammy ran

3 \frac{3}{5}

miles in

\frac{1 1}{2 0}

hour, which can be also written as

0.55

hour.

Pace in Miles per Hour

We want to determine Sammy's pace in miles per hour. We can do so by dividing the distance Sammy run by the time of the run.

Pace = \frac{Distance ( miles )}{Time ( hours )}

Let's substitute

3 \frac{3}{5}

miles for the distance and

\frac{1 1}{2 0}

hour for the time in our formula and simplify.

Pace = \frac{Distance ( miles )}{Time ( hours )}

SubstituteValues

Substitute values

Pace = \frac{3 \frac{3}{5}}{\frac{1 1}{2 0}}

MixedToFrac

$a \frac{b}{c} = \frac{a \cdot c + b}{c}$

Pace = \frac{\frac{1 8}{5}}{\frac{1 1}{2 0}}

DivFracByFracSL

$\frac{a}{b} / \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$

Pace = \frac{1 8}{5} \cdot \frac{2 0}{1 1}

▼

Simplify

MultFrac

Multiply fractions

Pace = \frac{1 8 \cdot 2 0}{5 \cdot 1 1}

Multiply

Pace = \frac{3 6 0}{5 5}

ReduceFrac

$\frac{a}{b} = \frac{a / 5}{b / 5}$

Pace = \frac{7 2}{1 1}

FracToMixed

Write fraction as a mixed number

Pace = 6 \frac{6}{1 1}

Sammy's pace is

6 \frac{6}{1 1}

miles per hour.

Exercise