in 10 days ethan can do as much work as jacob can do in 15 days to do a work together they take x days if jacob working alone can complete the work a 60 days then find the value of x?
Answers
Answer:
in 10 days ethan can do as much work as jacob can do in 15 days to do a work together they take x days if jacob working alone can complete the work a 60 days then find the value of x?
answer = 4 days
Given,
Ethan can do as much work in 10 days as Jacob can do in 15 days.
Together they take x days.
Time taken by Jacob alone to complete the work = 60 days
To find,
The time taken by both of them to complete the work or the value of x.
Solution,
The time taken by both of them to complete the work or the value of x will be 24 days.
We can easily solve this problem by following the given steps.
According to the question,
Time taken by Jacob alone to complete the work = 60 days
Ethan can do as much work in 10 days as Jacob can do in 15 days.
Jacob's work in 15 days = Ethan's work in 10 days
Jacob's work in 1 day = 10/15 days of Ethan's work
Jacob's work in 60 days =(10×60/15) days of Ethan's work
Jacob's work in 60 days =(600/15) days of Ethan's work
Jacob's work in 60 days = 40 days of Ethan's work
So, the time taken by Ethan to complete the work alone is 40 days.
Then, Ethan's work in 1 day = 1/40
And Jacob's work in 1 day = 1/60
According to the question,
Both of them can complete the work in x days.
Jacob's work in 1 day + Ethan's work in 1 day = 1/x
1/60 + 1/40 = 1/x
Taking the LCM of 60 and 40 which is 120 and adding the two fractions,
2+3/120 = 1/x
5/120 = 1/x
Using the cross multiplication method,
5x = 120
x = 120/5 ( 5 was in the multiplication on the left-hand side. So, it is in the division on the right-hand side.)
x = 24
Hence, the time taken by both of them to complete the work or the value of x is 24 days.