How would you solve this word problem?

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You rotate the tires on your truck, including the spare, so that all five tires are used equally. After 40,000 miles, how many miles has each tire been driven?

This is from Chalkdust Algrebra unit 1... Thanks!

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Is the answer 32,000 miles/tire? If not, please disregard.

If so, 40,000 car miles = 160,000 tire miles.

160,000/5 = 32000.

This sounds like a Singapore problem.

Terri

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Each of the five tires tire gets to be the spare for 1/5 of the total distance driven, i.e. for 8,000 miles.

So each tire has been driven for 32,000 miles.

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Each tire will be used 4/5 of the 40,000 miles. 4/5 * 40,000 is 32,000.

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Ok I get it now. Thank you!

I don't know how to type fractions but the solutions guide had:

40,000(4)

over

5

=

32,000

I needed to to the logic that each tire was driven 4/5 of the time. Duh! But, I wouldn't have understood w/out the help. :tongue_smilie:

Edited by LNC
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Ok I get it now. Thank you!

I don't know how to type fractions but the solutions guide had:

40,000(4)

over

5

=

32,000

I needed to to the logic that each tire was driven 4/5 of the time. Duh! But, I wouldn't have understood w/out the help. :tongue_smilie:

Just use a forward slash for fractions---> 40,000(4)/5

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You rotate the tires on your truck, including the spare, so that all five tires are used equally. After 40,000 miles, how many miles has each tire been driven?

This is from Chalkdust Algrebra unit 1... Thanks!

Since others have already answered the mathematical question, I will take the liberty of complaining about the wording of the problem. Warning: extreme pedantry follows. :lol:

It's impossible to rotate the tires so that all five tires are used equally AT ALL TIMES.

Say the tires are rotated every 8,000 miles. Then the five tires will go through one full rotation in 40,000 miles and each tire will have been driven 32,000 miles. But at every point up to the 40,000 they will not have been used equally.

If the tires are rotated every 4,000 miles, then the five tires will go through two full rotations in 40,000 miles.

Of course we all understand this. When one says the tires are rotated so that all are used equally, one means that overall the tires average to the same amount of use. But only at the final mile of a complete rotation is it true that they have had the exact same mileage.

On the other hand, if the tires were rotated every 3,000 miles, then at 30,000 all five tires will have been driven 24,000 miles. But at 40,000 they will have different mileages:

31,000

31,000

31,000

33,000

34,000

It won't be until 45,000 miles that they all have the same mileage again: 36,000.

So the problem makes the assumption that 40,000 miles is an integer multiple of the full rotation cycle. But they do not state that assumption! They write it as if at all times the tires have been equally used and that 40,000 miles is simply a particular mile to use for an example rather than quite a special one as a multiple of a full rotation.

The problem would have been better phrased as follows: You regularly rotate the tires on your truck, including the spare. After 40,000 miles, all five tires have been driven equally. How many miles has each tire been driven?

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You rotate the tires on your truck, including the spare, so that all five tires are used equally. After 40,000 miles, how many miles has each tire been driven?

This is from Chalkdust Algrebra unit 1... Thanks!

Like Cosmos, I have an objection too. The actual answer is 40,000 miles ... unless the spare was stored in the garage. :D

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What chapter is that problem? We're using Chalkdust and in unit one but haven't seen that one.

Also, Chalkdust has a solutions manual that not only gives the answer but shows how to solve for it.

Unit 1 review

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So the problem makes the assumption that 40,000 miles is an integer multiple of the full rotation cycle. But they do not state that assumption! They write it as if at all times the tires have been equally used and that 40,000 miles is simply a particular mile to use for an example rather than quite a special one as a multiple of a full rotation.

The problem would have been better phrased as follows: You regularly rotate the tires on your truck, including the spare. After 40,000 miles, all five tires have been driven equally. How many miles has each tire been driven?

:iagree: Part of learning to do word problems through K-12 grades and the first two years of college is not just about the math, but figuring out what simple concept the author who wrote the problem was going for. If you try to do these as engineering problems, looking as assumptions, etc, you will miss the simple concept and often come up with a different answer, which most instructors sadly will not take the time to think through and just count wrong.

After years of that, if a person goes on to engineering school, the habit of looking for the simple concept and jumping to that particular idea of what the problem is has to be unlearned, because now they are required to think of and write down every assumption that is being made, and lose credit if they skip that part.

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Like Cosmos' date=' I have an objection too. The actual answer is 40,000 miles ... unless the spare was stored in the garage. :D[/quote']

:lol:

That's the answer I would get at my house if I asked, and then this would turn into an hour-long debate about the exact meaning of the phrase "been driven."

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Each tire will be used 4/5 of the 40,000 miles. 4/5 * 40,000 is 32,000.

This is better than the book's answer.

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:lol:

That's the answer I would get at my house if I asked, and then this would turn into an hour-long debate about the exact meaning of the phrase "been driven."

:lol: You just described my house! DH, dd, middle ds, and myself spend a lot of time discussing the assumptions behind "real world problems" (which rarely turn out to be real world) and the potential meaning of any phrasing. Drive the eldest boy, not a math lover, batty! Youngest boy, 12, is now catching onto this.

As for reality, the spare would NOT be getting rotated!

Faith

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