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Ben starts walking along a path at
3mi//h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at
6mi//h. How long (in hours) will it be before Amanda catches up to Ben?
Enter the exact answer.
Hint: The distance formula is that distance
= rate
** time, so for example in one and a half hours, Ben has walked
3**1.5 miles.
Amanda catches up to Ben in
◻ hours.

Ben starts walking along a path at $3\,\text{mi/h}$ . One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at $6\,\text{mi/h}$ . How long (in hours) will it be before Amanda catches up to Ben? Enter the exact answer. Hint: The distance formula is that distance $=$ rate $\times$ time, so for example in one and a half hours, Ben has walked $3\times1.5$ miles. Amanda catches up to Ben in $\square$ hours.

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Ben starts walking along a path at

3\,\text{mi/h}

. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at

6\,\text{mi/h}

. How long (in hours) will it be before Amanda catches up to Ben? Enter the exact answer. Hint: The distance formula is that distance

=

rate

\times

time, so for example in one and a half hours, Ben has walked

3\times1.5

miles. Amanda catches up to Ben in

\square

hours.

Calculate Distance Traveled: Calculate the distance Ben has traveled by the time Amanda starts. $\newline$ Ben's speed = $3 \, \text{mi/h}$ , Time before Amanda starts = $1.5 \, \text{h}$ . $\newline$ Distance = Speed $\times$ Time = $3 \, \text{mi/h} \times 1.5 \, \text{h} = 4.5 \, \text{mi}$ .
Set Up Equation: Set up the equation to find when Amanda catches up to Ben. $\newline$ Let $t$ be the time in hours Amanda jogs to catch up to Ben. $\newline$ Amanda's speed = $6$ mi/h, Ben's speed = $3$ mi/h. $\newline$ Distance Amanda covers = $6t$ mi, Distance Ben covers = $4.5$ mi + $3t$ mi. $\newline$ Set distances equal to find $t$ : $6t = 4.5 + 3t$ .
Solve for t: Solve for t. $\newline$ $6t = 4.5 + 3t$ $\newline$ $6t - 3t = 4.5$ $\newline$ $3t = 4.5$ $\newline$ $t = \frac{4.5}{3}$ $\newline$ $t = 1.5$ hours.

More problems from Volume of cubes and rectangular prisms: word problems

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