tom takes 3days to do a piece of work while jerry takes only one day for the same. together, they both can finish the job in 15 days. in how many days tom will finish the work?
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I think the question should be reworded as: ...If it takes Tom & Jerry 15 days to finish the job, how many days will Tom finish the work? or something along these lines.
With that being said, the rate to do a piece of work from each:
Tom = 1/3 and Jerry = 1/1 or 1
Add: 1/3 + 1 = 1 1/3 or 4/3 (improper fraction)
4/3 * 15 = 20
This means that it will take 20 pieces of work to complete the job.
Therefore, Tom will finish the work in 20*3 = 60 days.
We see that Tom is a slow worker from the beginning and working alone will take him 60 days to complete the job.
To solve this problem, we can calculate the individual rates at which Tom and Jerry complete the work. Then we can use the combined rate to determine how long it would take Tom to complete the work alone.
Let's denote that Tom's rate is T pieces of work per day, and Jerry's rate is J pieces of work per day.
We are given that:
Tom takes 3 days to complete the work, so his rate is 1/3 (1 work in 3 days).
Jerry takes 1 day to complete the work, so his rate is 1/1 (1 work in 1 day).
Combined, they can finish the work in 15 days, so their combined rate is 1/15 (1 work in 15 days).
Now we can set up the equation:
Tom's rate + Jerry's rate = Combined rate
1/3 + 1/1 = 1/15
To solve this equation, we need to find a common denominator for 3 and 15, which is 15.
(1/3)*5/5 + 3/3 = 1/15
5/15 + 15/15 = 1/15
20/15 = 1/15
Now, we can compare the rates directly:
Tom's rate = 1/3
Combined rate = 1/15
Since Tom's rate is 1/3 and the combined rate is 1/15, we can calculate how long it would take Tom to complete the work alone by dividing the combined rate by Tom's rate:
1/15 รท 1/3 = 1/15 * 3/1 = 3/15 = 1/5
So, Tom will finish the work alone in 1/5 of a day or 1 day divided by 5, which equals 0.2 days or 0.2 * 24 = 4.8 hours.
Therefore, Tom will finish the work in approximately 4.8 hours or 0.2 days.
To find out how many days Tom will finish the work, let's first calculate the amount of work each of them does in a day.
Let's denote the total work to be done as W.
From the given information, we can calculate the following:
Tom does 1/3 of the work in a day (because he takes 3 days to complete it).
Jerry does 1/1 or the complete work in a day (since he takes only 1 day to complete it).
Now, let's assume Tom's work rate is T and Jerry's work rate is J, both measured in units of work per day.
Based on the information above, we can write the following equations:
T = 1/3W (Tom's work rate)
J = 1W (Jerry's work rate)
We are also given that they can finish the job together in 15 days. Let's denote the combined work rate of Tom and Jerry as R:
R = T + J
Since we know the work rate, we can calculate R:
R = 1/3W + 1W
R = (1 + 3)W / 3
R = 4W / 3
We are also given that they can complete the job in 15 days, so we can write:
15R = W
Substituting the value of R, we get:
15 * (4W / 3) = W
(60W / 3) = W
20W = 3W
W = 20
So, the total work is 20 units.
Now, to find out how many days Tom will finish the work alone, we can calculate his work rate (T) based on the total work:
T = 1/3W = 1/3 * 20 = 20/3
Therefore, Tom will finish the work alone in 20/3 days, which is approximately 6.67 days.