Find Number of Miles

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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.
 
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
 
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.
 
1. When I see a : b, I know this means a/b = a to b.[/1QUOTE]
NO! It means that if you were to divide the totality into a+ b equal parts, a of them would be one thing and b of them the other.
"The ratio of the number of miles Nash ran to the number of miles he walked improved 8:5" means that out of every 8+ 5= 13 miles he ran 8 miles and walked 5 miles. Of course to find the actual number of miles we would need to know the total number of miles walked and run. MathLover1 somehow discovered that the total was to be 26 miles. 26/13= 2 so dividing 26 into 13 parts, each part is 2 miles. He ran 8(2)= 16 miles and walked 5(2)= 10 miles. Of course 16+ 10= 26.

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.
You might want to get over that! Try THINKING about what the problem says, instead.

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?
26 miles is the length of one marathon. Of course, you don't necessarily one marathon's length each week to train for a marathon! This was your problem. What did IT say?

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!
Weak English? Poor reasoning skills? In word problems, you are not told what to do. You have to decide that yourself. Like making a "battle plan".
 
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
 


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