# A rate(maths) question?

Question:Mr Lim, working alone, takes 20 days to complete a job. Mr Tan, working alone, takes 15 days to complete the same job. If both work together for 6 days, what fraction of the job would be left?

can u pls show me the workings? cos i dun really understand how to do the question. thanks :)

For Mr. Lim:
6 days working / 20 days to complete => simplify the fraction to make it 3/10. Since 2 will go into 6 and 20 evenly you divide both numbers by 2 to simplify it.

For Mr. Tan:
6 days / 15 days = > simplify to make it 2/5. 3 will go into both 6 and 15 evenly and divide each number by 3 to simplify.

When you add 3/10 and 2/5, you need to change the 2/5 to make the bottom number (denominator) equal to the top number (numerator) -> 2/5 = 4/10. Add 3/10 and 4/10 and the fraction completed is 7/10. The fraction left to do still is the opposite which is 3/10.
Speed of Mr Lim = 1/20 job/day
Speed of Mr Tan = 1/15 job/day
Speed of Mr Lim + speed of Mr Tan
= (1/20 + 1/15) job/day
= (3/60 + 4/60) job/day
= 7/60 job/day

Amount of job done in 6 days by Mr Lim and Mr Tan
= (Speed of Mr Lim + speed of Mr Tan) x 6
= 7/60 x 6
= 7/10

Amount of job left
= 1 - Amount of job done in 6 days by Mr Lim and Mr Tan
= 1 - 7/10
= 3/10
Speed of Mr Lim = 1/20 job/day
Speed of Mr Tan = 1/15 job/day
Speed of Mr Lim + speed of Mr Tan
= (1/20 + 1/15) job/day
= 7/60 job/day

Amount of job done in 6 days by Mr Lim and Mr Tan
= 7/60 x 6
= 7/10

So, left would be 1-7/10 = 3/10 (Ans.)
Time taken by Lim = 20 days
Time taken by Tan = 15 days
Total time taken = x
Therefore,
1/20 + 1/15 = 1/x
(3 + 4) / 60 = 1/x Since, LCM of 15, 20 is 60.
7/60 = 1/x
x = 60/7 = 8 4/7 days (Mixed fraction)

How much is 6 days of 60/7 days?

[6 / (60/7) ] * 100
= [ (6 * 7) / 60 ] * 100
= (7/10) * 100 = 70 %

6 days is 70% of 60/7 days

So, 30% remains = 30/100 remains
= 3/10 of the job remains if both work for 6 days together

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