Henry can paint a house in 5 days and Jose can do the same work in 4 days. If they work together,how many days will it take them to paint the house?
Henry's rate = house/5
Jose's rate = house/4
combined rate = house/5 + house/4
= 9house/20
time at combined rate = house/(8house/20)
= house(20/8house)
= 20/8
= 2.5
it will take 2.5 days
To find out how many days it will take them to paint the house together, we can use the formula:
Work rate × Time = Amount of work
Let's denote Henry's work rate as H (which is equivalent to 1 house painted in 5 days) and Jose's work rate as J (which is equivalent to 1 house painted in 4 days).
Thus, we have:
H = 1/5 (since Henry can paint 1 house in 5 days)
J = 1/4 (since Jose can paint 1 house in 4 days)
Now, let's denote the time it takes them to paint the house together as T.
When they work together, their work rates are additive, so we have:
(H + J) × T = 1 (since together they can complete the entire work, which is painting 1 house)
Substituting the values for H and J, we get:
(1/5 + 1/4) × T = 1
To simplify the equation, we find a common denominator:
(4/20 + 5/20) × T = 1
(9/20) × T = 1
To isolate T, we can multiply both sides of the equation by the reciprocal of (9/20), which is (20/9):
(20/9) × (9/20) × T = (20/9) × 1
T = 20/9
Therefore, it will take them approximately 2.22 days (rounded to the nearest hundredth) to paint the house together.
To solve this problem, we need to calculate how much work each person can do in one day. Then we can add their rates of work together to find the combined rate. Finally, we can use the combined rate to determine how many days it will take to complete the job.
Let's start by finding out how much work Henry can do in one day. Since Henry can paint a house in 5 days, his rate of work is 1/5 of a house per day.
Similarly, Jose can paint a house in 4 days, so his rate of work is 1/4 of a house per day.
To find how much work they can do together in one day, we will add their rates of work:
1/5 (Henry's rate of work) + 1/4 (Jose's rate of work) = (4 + 5) / 20 = 9/20 of a house per day.
So, together, they can paint 9/20 of a house in one day.
To determine how many days it will take for them to paint the whole house, we can divide the total work (1 house) by their combined rate of work (9/20 of a house per day):
1 / (9/20) = 20/9 ≈ 2.22 days.
Therefore, it will take them approximately 2.22 days to paint the house if they work together.