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### Course: 6th grade (Eureka Math/EngageNY)>Unit 1

Lesson 3: Topic C: Unit rates

# 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?
• Henry can write 1,480 pages in 888 hours.
(Thanks for the practice!)
• are rates and ratios similar
• 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.
• 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?
• 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 rounded decimal, or truncated, it 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
? pages to 8 hours = p to 8

★ p to 8
and 5 to 3
=
p/8 = 5/3
←ratios in proportion
=
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 full pages, the author completes 13 whole pages per 8 hours.

(≧▽≦) I hope this helps.
• Does anyone still go on here?
• I still go on here.
• Test 1.2.3 mic check 1.2.3
• I mean, this isn’t a question and neither am I tryna be mean; it’s just that - it’s math. Math is math.
• What about related rates? How do we apply differential calculus for related rates?
• 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.
• comment if your seeing this in April 15, 2023