Mathematics
Grade6
Easy
Question
Paul can eat 5 hot dogs in 10 minutes. _________ minutes are taken by him to eat 30 hot dogs
- 60
- 90
- 50
- 50
Hint:
We are given the time required by Paul to eat 5 hot dogs. It is 10 minutes. We are asked to find the time required by Paul to eat 30 hot dogs, given the rate is same. To solve this question, we will find the rate first. We will find the rate using the first data. Once we find the rate, we can find the required quantity.
The correct answer is: 60
Let the number of hot dogs be denoted by N.
So the given values of number of hot dogs and time are:
N = 5
Time = 10 minutes
Using this data, we will find the rate. We will find the rate by taking the ratio of number of hot dogs to the time. As rate is constant, we will use this to find the time required by Paul to eat 30 hot dogs.
![R a t e equals space fraction numerator N over denominator T i m e end fraction
space space space space space space space space equals 5 over 10
space space space space space space space space equals 1 half h o t d o g s space p e r space m i n u t e](data:image/png;base64,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)
Now using the value of rate we will find the time required
We will rearrange the expression for time.
![T i m e equals fraction numerator N space over denominator R a t e end fraction
space space space space space space space space space equals fraction numerator 30 over denominator begin display style 1 half end style end fraction
space space space space space space space space space equals space 60 space m i n u t e s](data:image/png;base64,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)
So, Paul takes 60 minutes to eat 30 hot dogs.
The other method is to take the ratios and directly equate them. As the rate is constant, so the ratios will be constant. So we will consider the quantity we have to find as x and then equate the ratios. It will be a shortcut.