Math  /  Algebra

Questionenuity com/player/
Using a Proportion to Complete a Table \begin{tabular}{|c|c|} \hline Miles & Minutes \\ \hline 1 & 7 \\ \hline 3 & 21 \\ \hline 7 & aa \\ \hlinebb & 70 \\ \hline 15 & cc \\ \hline \end{tabular}
Martin's running ability is measured by this proportion: 17=321\frac{1}{7}=\frac{3}{21}
Use the proportion to identify the values of the variables that complete the rate table a=\mathrm{a}= \square b=b= \square c=c= \square Done

Studdy Solution

STEP 1

What is this asking? We need to find how many minutes it takes Martin to run different distances based on his constant running speed. Watch out! Make sure the units match in your calculations – we're dealing with miles and minutes!

STEP 2

1. Find *a* (minutes to run 7 miles)
2. Find *b* (miles run in 70 minutes)
3. Find *c* (minutes to run 15 miles)

STEP 3

We know Martin runs 1 mile in 7 minutes.
We want to find how many minutes (aa) it takes him to run 7 miles.
We can set up a proportion: 1 mile7 minutes=7 milesa minutes\frac{1 \text{ mile}}{7 \text{ minutes}} = \frac{7 \text{ miles}}{a \text{ minutes}}

STEP 4

To solve for aa, we can **cross-multiply**: 1a=771 \cdot a = 7 \cdot 7 a=49a = 49So, it takes Martin **49** minutes to run 7 miles!

STEP 5

We still know Martin runs 1 mile in 7 minutes.
Now, we want to find how many miles (bb) he runs in 70 minutes.
Let's set up another proportion: 1 mile7 minutes=b miles70 minutes\frac{1 \text{ mile}}{7 \text{ minutes}} = \frac{b \text{ miles}}{70 \text{ minutes}}

STEP 6

**Cross-multiply** to solve for bb: 170=7b1 \cdot 70 = 7 \cdot b 70=7b70 = 7bTo isolate bb, we **divide both sides by 7**: 707=7b7\frac{70}{7} = \frac{7b}{7} 10=b10 = bMartin runs **10** miles in 70 minutes!

STEP 7

One last time, we use the fact that Martin runs 1 mile in 7 minutes.
We want to know how many minutes (cc) it takes him to run 15 miles.
Our proportion is: 1 mile7 minutes=15 milesc minutes\frac{1 \text{ mile}}{7 \text{ minutes}} = \frac{15 \text{ miles}}{c \text{ minutes}}

STEP 8

**Cross-multiply**: 1c=7151 \cdot c = 7 \cdot 15 c=105c = 105It takes Martin **105** minutes to run 15 miles.

STEP 9

a=49a = 49 b=10b = 10 c=105c = 105

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