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### Unit 2: Lesson 11

Lesson 12: Navigating a table of equivalent ratios

# Rate problems

Sal uses rates to solve word problems. For example, Lynette can wash 95 cars in 5 days. How many cars can Lynette wash in 11 days?

## 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.
• Does anyone still go on here?
• Yes their are tons of people still on Khan Academy :)
• Test 1.2.3 mic check 1.2.3
• this isn't music class, sorry to break it to ya </3
• 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.
• I still don’t understand rate problems. Can someone help please?

Thank you!
• is my toes humungas?
• I don't know what this is actually meant to mean but, yes, yes they are.
• I don't get it why do we have to divide 95 days by 11 and 5 day by 11