Jim and his dad are bricklayers. Jim can lay bricks for a fireplace and chimney in 5 days. With his father's help he can build it in 2 days. How long would it take his father to build it alone?
Jim's rate --- 1/5
dad's rate --- 1/x
combined rate = 1/5 + 1/x
= (x+5)/(5x)
given: (x+5)/(5x) = 1/2
5x = 2x + 10
3x = 10
x = 10/3
so by himself dad could build it in 3 1/3 days
To solve this problem, we can use the concept of "work rates".
Let's say Jim's work rate is J, and his father's work rate is F.
We know that Jim can complete the work in 5 days, so his work rate is 1 job per 5 days or J = 1/5.
With his father's help, they can complete the work in 2 days, so their combined work rate is 1 job per 2 days or (J + F) = 1/2.
To find his father's work rate, we subtract Jim's work rate from the combined work rate:
F = (J + F) - J = 1/2 - 1/5
To subtract fractions, we need a common denominator, which in this case is 10.
F = (5/10) - (2/10) = 3/10
So, his father's work rate is 3/10, which means he can complete 3/10 of the job per day.
To find out how long it would take his father to build it alone, we use the formula:
Time = Work / Rate
Since the father's work rate is 3/10 and the job is 1, we have:
Time = 1 / (3/10)
To divide by a fraction, we invert and multiply:
Time = 1 * (10/3) = 10/3
Therefore, it would take Jim's father 10/3 days or approximately 3 1/3 days to build the fireplace and chimney alone.