Main content

### Course: 7th grade > Unit 5

Lesson 6: Rational number word problems- Rational number word problem: school report
- Rational number word problem: cosmetics
- Rational number word problem: cab
- Rational number word problem: ice
- Rational number word problem: computers
- Rational number word problem: stock
- Rational number word problem: checking account
- Rational number word problems

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Rational number word problem: cosmetics

Remember units of measurement? Convert minutes into hours and put your knowledge of fractions to work in this word problem. Created by Sal Khan.

## Want to join the conversation?

- How do you figure out the cost of a meal before tax if you only have the cost after tax? This is where my practice problems told me to go when I got stuck.(13 votes)
- Well, if you have the tax %, then you could do it. All you would have to do is multiply the tax % by the total cost. You would then subtract what you got from the total cost and you would have the cost before tax.

Hope this helps.(18 votes)

- Please someone explain this for me.

Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position.

Julian sets the simulated biker to a speed of 20km/h. After he rides his bike for 15 minutes, Julian's app reports a position of -2 1/4 km

What has Julian's average speed been so far?(5 votes)- Ok so in this situation we have the rate of speed of the simulated biker (20km/h) how long the simulated biker and Julian have traveled for (15 minutes) and how far Julian is behind the simulated biker (-2 1/4 km). The first step is to figure out how far the simulated biker has gone. Speed is simply distance over time so if we multiply our simulated biker's rate by the time it has been riding we get its distance. However, our time is in minutes so we must convert it to hours. To do this we divide it by 60, which gives us 0.25 or one quarter hour. 20km per hour times 1/4 hour gives us 5km, which is the distance the simulated biker has traveled.

Now we can figure out how far Julian has traveled, he is 2 1/4 km behind the simulated biker so 5 km - 2 1/4 km gives us Julian's distance of 2 3/4 km. Since we know Julian traveled this distance in 15 minutes his rate is (2 3/4 km)/(1/4 h) since we already know 15 minutes is a quarter hour. Now we have to get it to be over a whole hour, so we multiply the fraction by 4/4, which works because a number divided by itself is equal to 1. 2 3/4 * 4 can be done by turning 2 3/4 into the improper fraction 11/4 * 4, which gives us 44/4 km or just 11km and 1/4 h times 4 is just 1h. So our final answer of Julian's average speed is 11km/h.(11 votes)

- is there a faster way?(6 votes)
- Theres always a faster way cause everyone has a different way of solving problems(8 votes)

- I've watched every single video on Rational number word problems and I am still very confused. Can someone please help me?(5 votes)
- I agree with Nathan106. I, too, have watched every video multiple times and they have no seeming relation to the questions in the quiz.(0 votes)

- 2400mins/1 person = x mins/8 people

(8people * 2400mins)/1 person = x mins

Can someone explain why setting up a ratio would not work here?(3 votes)- You have 2 ratios: 2400mins/1 person and x mins/8 people

When 2 ratios are set equal to each other it is called a proportion.

The common method for solving proportions is to cross multiple as you have done.(2 votes)

- hii uh i dont get this .-.(3 votes)
- would it really matter the amount of people there are by making the gift bags if it only took Jess only 2 minutes?(3 votes)
- Hello teacher!

Why can't the formula t=w/r. be used in this topic?

I think it should be t=1200/2=600min

How should I avoid such a mistake and can you give me a tip on how to use this formula? Thank you very much!

(My English is not my first language and I think maybe it's because of translation problems with some of the words that I don't know how to solve the questions)

What I mean is: can you help me write down how the title asks me if I can use this formula?thank you very much！(2 votes)- 1200 is not a unit of work. Think of what you are doing with the units 1200 bags/(2 mins/1 bag), flip the bottom to get 1200 bags * 1 bag/2 mins and you get 600 bag^2/min which units do not make any sense to me. You incorrectly found the units to be minutes.(2 votes)

- How come I'm still confused after watching all of these videos to help me do "Rational Word Problem"? This makes me a little confused.(2 votes)
- These are all rational problems, and it shows you strategies you can use.(1 vote)

- thanks a lot for the videos because they really help me i dont know what i would do without them :))

yes i know sorry this is not a question but thanks

(^-^)(2 votes)

## Video transcript

Jess recently started a business
producing cosmetic products made from natural ingredients. She wants to
advertise her products by distributing bags of
samples in her neighborhood. She calculated that it
takes her two minutes to prepare each bag. How many hours--
they give us minutes here, now they want
hours-- how many hours will it take to prepare
1,200 bags of samples if she asks seven friends
to help her with her work? So the one thing we
could think about is, how long would it take
her to do it by herself? So it takes her, by herself,
two minutes per bag. And then we have 1,200 bags,
not 12 bags, 1,200 bags which means it's going to
take her two minutes for each of the 1,200 bags. Well that's 2 times
1,200 is 2,400 minutes. Now that's if she was just
working on it by herself, but she's got seven friends. And we can assume
that they would all take about two minutes
to prepare each bag. Now this is a little
bit tricky because you might want to divide
this by 7 saying, hey, we're going to have seven
times as many people. But you remember, she
asks seven friends so there's actually
eight people involved. There's Jess and
her seven friends. So it's actually going
to be eight times faster than if Jess did it by herself. This is if she only
had one person. If you're going to
have eight people, you are going to take
eight times less time. So with eight people, it's
going to be 2,400 divided by 8 is 300 minutes. And we're almost done, except
for the fact that they asked for our answer in
terms of hours. So 300 minutes is
how many hours? Well you have 60
minutes per hour so you could say 300
minutes-- I'll just write min for short-- divided
by 60 minutes per hour gives us 300 divided
by 60 is 5 hours. So it will take Jess and her
seven friends, a total of eight people, five hours to prepare
all of her sample bags.