Mathematics
Grade6
Easy
Question
Jake takes 18 minutes to finish reading 5 pages of a book. Determine the time taken by him to complete 30 pages in minutes
- 100
- 101
- 108
- 103
Hint:
In this question, we are given the time Jake takes to read 5 pages. It is 18 minutes. Using this data, we are asked to find the time taken by him to read 30 pages, given the rate is constant. We can try to find an equation using these quantities to get the value.
The correct answer is: 108
The given value for the number of pages and time are as follows:
Let ‘N’ denote the number of pages.
N = 5 pages
Time = 18 minutes.
We have to find out the rate at which Jake is reading the book. We have to take ratio of number of pages and time. As the given speed is constant, we can use this value to find the time required to read 30 pages.
We know the formula for speed.
![S p e e d space equals fraction numerator N over denominator T i m e end fraction
S u b s t i t u t i n g space t h e space v a l u e s comma space w e space g e t
S p e e d space equals 5 over 18](data:image/png;base64,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)
Now, using the speed, we will calculate the time required to read 30 pages.
We have to find the time required to read 30 pages.
Let’s see the formula.
. ![S p e e d space equals fraction numerator N over denominator T i m e end fraction
R e a r r a n g i n g space t h e space f o r m u l a space t o space f i n d space t i m e. space
W e space w i l l space m u l t i p l y space b o t h space s i d e s space b y space t i m e space a n d space d i v i d e space b y space s p e e d.
T i m e space equals fraction numerator N over denominator S p e e d end fraction
space space space space space space space space space space equals fraction numerator 30 over denominator begin display style 5 over 18 end style end fraction
space space space space space space space space space space equals space fraction numerator 30 space cross times space 18 over denominator 5 end fraction
space space space space space space space space space space equals 108 space m i n u t e s 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Therefore, the time required to read 30 pages is 108 minutes.
So the option which is ‘108’, is the right option.
We have to be careful about the units. Same quantities must have same units.