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?
days hours
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
in two days, Jim does 2/5 of the job, so his dad does 3/5
3/5 in two days means 5/5 (the whole thing) in ... 2 * 5/3 days
@Reiny my apologies, I did copy and paste
T1 = 5 days = Jim's time.
T2 = Father's time.
T1*T2(T1+T2) = 2.
5*T2/(5+T2) = 2,
5T2 = 10+2T2,
T2 = 3 1/3.
Thanks all of you
To figure out how long it would take Jim's father to build the fireplace and chimney alone, we can use the concept of work rate.
Let's say Jim's work rate is represented by the variable "J," and his father's work rate is represented by the variable "F."
From the given information, we know that Jim can build the fireplace and chimney alone in 5 days. Therefore, his work rate is 1 fireplace and chimney per 5 days, or J = 1/5.
When Jim and his father work together, they can complete the job in 2 days. The combined work rate is obtained by adding their individual work rates, so we have J + F = 1/2.
Now, we can use these two equations to find the value of F, which represents Jim's father's work rate.
Firstly, substitute J = 1/5 into the combined work rate equation:
(1/5) + F = 1/2
Next, we can simplify this equation:
F = 1/2 - 1/5
To calculate this, we need to find a common denominator:
F = (5/10) - (2/10)
F = 3/10
So, Jim's father can build the fireplace and chimney alone at a work rate of 3/10.
To determine how long it would take him to complete the job alone, we need to invert the work rate (since it represents the fraction of the job completed per day):
1 / (3/10) = 10/3
Therefore, it would take Jim's father approximately 10/3 days to build the fireplace and chimney alone, which is equivalent to 3 and 1/3 days, or approximately 3 days and 8 hours.
I posted the above reply yesterday to this same question.
You just cut-and-pasted my answer word for word and made it your own.
Not cool!