Find Number of Miles

In the fifth week, the ratio of the number of miles Nash ran to the number of miles he walked improved 8:5. How many miles did Nash run in week five?

Let me see.

We know that 8:5 means 8 miles by 3 miles.

One mile = 5280 feet.

Let R = number of miles that Nash ran in week 5.

R = 8(5280)/[5(5280)]

R = 40

 

how do you know that 8:5 means 8 miles by 3 miles>
One mile = 5280 feet.-> why you need this?


Ratio of miles ran to miles Walked is 8:5
Thus, we can obtain the miles ran by Nash in the 5th week as follow:

Ratio ran = 8
Ratio walked = 5
Total ratio = 8 + 5 = 13

Miles per week for training = 26 mile
Mile ran in the 5th week = 8/13 × 26
Mile ran in the 5th week = 8 × 2
Mile ran in the 5th week = 16 miles

Therefore, Nash ran 16 miles in the 5th week of training.

 

1. When I see a : b, I know this means a/b = a to b.

2. I didn't pay close attention to the words ran and walked.

3. When I see the word mile or miles in applications, I assume that somewhere along the way, I will need to use the fact that one mile is the same as 5,280 feet.

4. Why did you add the ratios?

5. Where did you get 26 miles?

6. What information in the problem said to calculate
(ran)/(total ratios) times 26?

Do you understand why I struggle with word problems? By the way, this is a middle school application. It's funny to know that a person reviewing precalculus struggles with grades 6 through 12 applications. Ha!

 

4. Why did you add the ratios?
imagine one line segment, if you need to divide it in 2 parts in ratio is 8:5 , you know there will be 8+5=13 certain equal lengths (one part will be 8 of these certain equal lengths, the other part will be 5 of these certain equal lengths)
see example:


5. you didn't post entire question which is:
Nash is training for a marathon and decides to train for 26 miles every week. In the first week, the ratio of the number of miles he ran to the number of miles he walked 3:10.
In the fifth week the ration ran to walked is 8:5. How many miles did Nash run in week 5

 

Thank you breaking down the question this way.

 

Who has time for a battle plan when taking a timed test? I recall my school days.

 

The shorter the test is the more you need a "battle plan"!

 

Correction: Needed a battle plan. Country Boy, I am 56 years old. I am not a student. My student days ended in 1994. I do this just for fun.

 

nycmathguy, you're just a child compared to most of us here.

 

Really? Are you serious? I am 56 going on 80, physically speaking. A child? At 56, a child?

 

I'm 77, walk with a cane and use a magnifying glass to read.

 

You made it into your late 70s. Congratulations! Look what happened to Bob Saget. Dead at 65. What happened? Booster shot? COVID-19? Vaccines?

 

the official cause of death will take weeks to determine
there is no need to speculate

 

True but people are dropping like flies after taking the vaccines.