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# 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.
• 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.
• 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?
• 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.
• is there a faster way?
• Theres always a faster way cause everyone has a different way of solving problems
• I've watched every single video on Rational number word problems and I am still very confused. Can someone please help me?
• I agree with Nathan106. I, too, have watched every video multiple times and they have no seeming relation to the questions in the quiz.
• 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?
• 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.
• hii uh i dont get this .-.
• 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.
• These are all rational problems, and it shows you strategies you can use.
(1 vote)
• 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！
• 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.
(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

(^-^)