Tom takes 3 days 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?
I do not understand either.
To solve this problem, we can use the concept of work rates.
Let's say Tom's work rate is T units per day, and Jerry's work rate is J units per day.
We are given that Tom takes 3 days to complete the work, so we can say that Tom's work rate is 1/3 units per day (since he completes 1 work in 3 days).
We are also given that Jerry takes 1 day to complete the work, so Jerry's work rate is 1 unit per day.
Let's assume that, when working together, their combined work rate is R units per day.
According to the problem, together they can finish the job in 15 days. This means that their combined work rate is 1/15 units per day.
Using the information above, we can set up the equation:
T + J = R --(1)
And we know that T = 1/3 and J = 1, so we can substitute these values into equation (1):
1/3 + 1 = R
Multiplying both sides of the equation by 3 to eliminate the fraction:
1 + 3 = 3R
4 = 3R
Dividing both sides of the equation by 3:
4/3 = R
So, when they work together, their combined work rate is 4/3 units per day.
Now, we can determine how many days it will take Tom to finish the work by himself. Let's assume that Tom can complete the work in x days.
Since Tom's work rate is 1/3 units per day, we can set up the equation:
1/3 * x = 1
Multiplying both sides of the equation by 3 to eliminate the fraction:
x = 3
Therefore, Tom will finish the work in 3 days.