Pre-Algebra Question: "As part of an annual fundraiser to help raise money for diabetes research, Linda joined a bikeathon...."

[youlanda punch]

As part of an annual fundraiser to help raise money for diabetes research, Linda joined a bikeathon. The track she biked on was 1408 yd long. Linda biked 32.5 laps. Her sponsors agreed to donate an amount of money for each mile she biked. How many miles did she bike?

 

[Otis]

Hi youlanda punch. Where did you get stuck? Do you need help converting yards to miles? Please share your work so far.

 

[The Highlander]

If length conversion is your problem then a useful calculator can be found here.

 

[Steven G]

Can you figure out how far Linda biked?
Now convert that number of yards to miles.
Note that 1 mile equals 1,760 yds

 

[Otis]

… The track she biked on [is] 1408 yd long. Linda biked 32.5 laps. …How many miles did she bike?

We hope youlanda punch was able to solve the exercise. Here's my work, for other readers.

Linda biked 1,408 yards, and she did that 32.5 times. Therefore, calculating the total yardage is a multiplication problem.

1408 × 32.5 = 45760

Linda biked a total of 45,760 yards. The exercise asks us to report this distance in miles, so we convert the yardage to miles.

Steven told us that 1,760 yards is 1 mile. How many 1,760 yard lengths are there in 45,760 yards? (Each one is a mile.) That's a division problem.

45760/1760 = 26

Linda biked a total of 26 miles.

 

[Otis]

Dimensional analysis is another way of doing unit conversions. In that method, we form conversion ratios and then cancel units (similar to how we cancel common factors when multiplying fractions). In the following example, I'll convert 45,760 yards to miles using the knowledge that 1 yard is 3 feet and 1 mile is 5,280 feet.

\(\displaystyle \frac{45760\text{ yard}}{1} \;\times\; \frac{3\text{ foot}}{1\text{ yard}} \;\times\; \frac{1\text{ mile}}{5280\text{ foot}}\)

\(\displaystyle \frac{45760\;\cancel{ yard}}{1} \;\times\; \frac{3\;\cancel{ foot}}{1\;\cancel{ yard}} \;\times\; \frac{1\text{ mile}}{5280\;\cancel{ foot}}\)

\(\displaystyle \frac{45760\;\times\;\cancel{3}^1\;\times\;1\text{ mile}}{1\;\times\;1\;\times\;\cancel{5280}_{1760}}\)

\(\displaystyle \frac{45760\text{ mile}}{1760}\;=\;26\text{ mile}\)

 

[lookagain]

\(\displaystyle \frac{45760\text{ yards}}{1} \;\times\; \frac{3\text{ feet}}{1\text{ yard}} \;\times\; \frac{1\text{ mile}}{5280\text{ feet}}\)

\(\displaystyle \frac{45760\;\cancel{ yards}}{1} \;\times\; \frac{3\;\cancel{ feet}}{1\;\cancel{ yard}} \;\times\; \frac{1\text{ mile}}{5280\;\cancel{ feet}}\)

\(\displaystyle \frac{45760\;\times\;\cancel{3}^1\;\times\;1\text{ mile}}{1\;\times\;1\;\times\;\cancel{5280}_{1760}}\)

\(\displaystyle \frac{45760}{1706}\;=\;26\text{ mile}\)

The above corrections in the quote box were made on a computer tablet.
They are the plurals of the units and the addition of the missing unit of
"miles" for the fraction at the bottom left of the page.

 

[Otis]

missing unit

Thanks for noting that. I'll get it fixed.

 

[khansaheb]

Dimensional analysis is another way of doing unit conversions. In that method, we form conversion ratios and then cancel units (similar to how we cancel common factors when multiplying fractions). In the following example, I'll convert 45,760 yards to miles using the knowledge that 1 yard is 3 feet and 1 mile is 5,280 feet.

\(\displaystyle \frac{45760\text{ yard}}{1} \;\times\; \frac{3\text{ foot}}{1\text{ yard}} \;\times\; \frac{1\text{ mile}}{5280\text{ foot}}\)

\(\displaystyle \frac{45760\;\cancel{ yard}}{1} \;\times\; \frac{3\;\cancel{ foot}}{1\;\cancel{ yard}} \;\times\; \frac{1\text{ mile}}{5280\;\cancel{ foot}}\)

\(\displaystyle \frac{45760\;\times\;\cancel{3}^1\;\times\;1\text{ mile}}{1\;\times\;1\;\times\;\cancel{5280}_{1760}}\)

\(\displaystyle \frac{45760\text{ mile}}{1706}\;=\;26\text{ mile}\)

Minor "thunder-finger":
The denominator of the last line should be 1760 (instead of 1706).

 

[Otis]

denominator of the last line should be 1760

Fixed, thank you.