Mike can complete a project in 60 minutes͵ and if Mike and Walter both work on the project͵ they can complete it in 40 minutes. How long will it take Walter to complete the project by himself?
Mike (1/60) project/min
Walter (w project/min)
together
(1 + 60 w)/60 project /min
[(1+60 w)/60 ] 40 = 1 project
1 + 60 w = 6/4
60 w = .5
w = .0083333
1/w = min/project = 120 minutes
To solve this problem, we can use the concept of work. The rate at which work is done is the reciprocal of the time it takes to do the work. Let's say Mike's work rate is Rm (in units of work per minute) and Walter's work rate is Rw.
Given that Mike can complete the project in 60 minutes, his work rate can be calculated as:
Rm = 1 / 60
Let's assume that Walter takes x minutes to complete the project by himself. In x minutes, Walter does 1 unit of work:
Rw = 1 / x
Now, if Mike and Walter work on the project together, they can complete it in 40 minutes. In 40 minutes, the combined work of Mike and Walter is 1 unit:
(Rm + Rw) * 40 = 1
Substituting the values of Rm and Rw, we have:
(1 / 60 + 1 / x) * 40 = 1
Now, let's solve this equation for x, which represents the time it takes Walter to complete the project by himself.
First, multiply both sides of the equation by x:
40 + 40x / 60 = x
Simplifying the left side of the equation:
40 + (2/3)x = x
Get rid of the fractions by multiplying through by 3:
120 + 2x = 3x
Rearranging the terms:
2x - 3x = -120
-x = -120
Dividing by -1:
x = 120
Therefore, it will take Walter 120 minutes to complete the project by himself.
Let's assume Walter takes x minutes to complete the project by himself.
The rate at which Mike completes the project is 1 project per 60 minutes, or 1/60 project per minute.
The combined rate at which Mike and Walter complete the project is 1 project per 40 minutes, or 1/40 project per minute.
Since rate is equal to the reciprocal of time, we can write the equation:
1/60 + 1/x = 1/40
To solve for x, we can cross-multiply:
40x + 60(40) = 60x
40x + 2400 = 60x
2400 = 60x - 40x
2400 = 20x
Dividing both sides by 20:
x = 2400 / 20
x = 120
Therefore, it will take Walter 120 minutes to complete the project by himself.