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# Rate problems

In this math lesson, we learn to find unit rates and use them to solve problems. We first calculate the rate for one unit, like cars washed per day or cost per battery. Then, we multiply the unit rate by the desired quantity to find the answer. This method simplifies complex problems and helps us understand real-world situations.

## Want to join the conversation?

- Henry can write 555 pages of his novel in 333 hours.

At this rate, how many pages can Henry write in 888 hours?(19 votes)- Henry can write 1,480 pages in 888 hours.

*(Thanks for the practice!)*(58 votes)

- are rates and ratios similar(16 votes)
- The word and the roots have the same meaning. But the difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.(24 votes)

- Fact" Author writes 5 pages in 3 hours

3 hours= 3x60= 180 minutes .

he writes 5 pages in 180 minutes ...

Divide 180 by 5, so he takes 36 minutes to write one page.

Thew Question: how many pages can he write in 8 hours?

8x 60 is 480 minutes.

Then divides minutes per page into available (5 hours) minutes, so..

480 divided by 36 is 13.3333 etc. But evidently that's not correct.

Where did I go wrong?(8 votes)**Great documentation of the method and reasoning you used**!**You are correct****in your calculations and conclusions**, so probably just needed the.**answer in a different form****Since**13.333333… must be written as**a**, or truncated, it*rounded*decimal**becomes an**.*approximation*

It's likely the answer needed to be entered as**an exact equal value**, rather than a rounded 'close to correct' decimal.

★ Here's an**easy way**to arrive at the answer…**Set the**.*ratios in proportion*to each other

Put**both ratios in the same order**.

You can arrange them either way, as long as*both ratios match*.

Let's go with…**Pages to Hours**

An author writes at a rate of:**5 pages to 3 hours = 5 to 3**

How many pages in 8 hours?**p = pages**and

? pages to 8 hours = p to 8

★ p to 8**5 to 3**←ratios in proportion

=

p/8 = 5/3

=

cross multiply

=**3p = 8 • 5**←🥳

=

3p = 40

=

p = 40/3 pages in 8 hours

=

p = 13 1/3 pages in 8 hours

≈

p ≈ 13.333333…

The author writes thirteen and one third pages per eight hours.

•**Fraction form 40/3 is an exact answer**(some say improper fraction because numerator is larger than denominator)

•**Mixed Number form**:**13 1/3**, sometimes used as an answer,**if directly asked for in the directions**, mathematically it means 13+1/3.

•If they want**how many**, the author*full pages**completes***13**per 8 hours.*whole*pages

(≧▽≦) I hope this helps.(22 votes)

- Does anyone still go on here?(15 votes)
- I still go on here.(6 votes)

- Test 1.2.3 mic check 1.2.3(10 votes)
- I mean, this isn’t a question and neither am I tryna be mean; it’s just that - it’s math. Math is math.(9 votes)
- What about related rates? How do we apply differential calculus for related rates?(6 votes)
- In all cases, you can solve the related rates problem by taking the derivative of both sides, plugging in all the known values (namely, x, y, and ˙x), and then solving for ˙y.(4 votes)

- comment if your seeing this in April 15, 2023(5 votes)
- can I just say that rates are way to easy(5 votes)
- I don't get it why do we have to divide 95 days by 11 and 5 day by 11(4 votes)
- you need to divide 95 by 5 not eleven because 95 divided by 5 is 19 which is the number of cars linete washes in one day and then you
*multiply*that by 11 to get how much cars he washes in 11 days.(4 votes)

## Video transcript

- [Instructor] So we're told
that Lynnette can wash 95 cars in five days. How many cars can
Lynnette wash in 11 days? So like always, pause this video and see if you can figure this out. So the way that I would like to tackle it is given the information they
gave us, 95 cars in five days, can we figure out how many
cars she can wash per day? How many cars in one day? And then we could just multiply that by 11 to figure out how many
she could wash in 11 days. So there's 95 cars in five days and so instead of five, if we were to say one day, one day, well, to go from five days to
one day, we divide by five. So the number of cars
she can do in one day, that would be that divided by five. In either case, we would divide by five and what's 95 divided by five? You might recognize that well, look, five times 20 is equal to 100. So five times 19 is 95. So you might recognize
that's 19 cars in one day or if that math I just did
seems a little bit too fast, you could just take five into 95. Five goes into nine one
time, one times five is five, subtract, nine minus five is
four, bring down that five, five goes into 45 nine
times, nine times five is 45 and it goes in perfectly. There's no remainder. So all I did is I divided
both of these numbers by five to figure out how many
she can wash per day. So she can wash 19 cars in
one day, 19 cars per day and so if I wanna figure out how many she can wash in
11 days, so in 11 days, well, now, I am just multiplying by 11. So if I multiply 19 times
11, what am I going to get? Well, if you're good at
the mental mathematics, you might recognize 19
times 10 would be 190 and then you would have one more 19 so that would be 209 cars or you could just multiply 19 times 11. One times 19 is 19 and
then one times 19 is 19. Add 'em together, you get 209. So she can wash 209 cars in 11 days. Let's do another example. Here, we are told at the market,
eight batteries cost $10. How much do six batteries cost? Once again, pause this video
and try to figure it out. Well, I'm gonna do the same technique. If eight batteries cost $10, let's figure out how
much one battery costs. So one battery costs what? Figure that out. Well, it's going to be 1/8th. To go from eight to
one, I divide by eight. So what happens when I divide 10 by eight? That's gonna be my per battery cost. So 10 divided by eight
is the same thing as 5/4 which is the same thing as one and 1/4 which is the same thing if
we're talking in terms of money, it might be more useful to write it like one and 25 hundredths or one battery costs $1.25. And so when they're saying six batteries, how much do six batteries cost, well, if we're going
to six batteries cost, we're multiplying the number
of batteries times six now. So what's $1.25 times six? So it's gonna be $6 plus another $1.50 'cause six times 25 is 150. So it's gonna be $7.50 and just to make sure the
math I just did was right, let's multiply $1.25 times six. Six times five is 30. Six times two is 12 plus three is 15. Six times one is six plus one is seven and we have a total of two
digits behind the decimal so there you have it, you have $7.50. Now, there's other ways
that you could tackle this. You could say that hey, this is, six batteries is gonna cost 6/8ths as much as eight batteries but that's a little bit
confusing, at least for my brain. I like to go just down to
the unit cost you could say, the cost per battery and
then multiply it by six. It gives me more comfort in
understanding what I'm doing.