it takes bill 4 hours to paint a house. it takes john 7 hours to paint the same house. how long does it take to paint the house if they painted it together.
If you put the name of the subject then the correct teacher can give you help more quickly.
Area of the house to be painted = A
Bill pains "B" area per hour
John pains "J" area per hour
So, A/B = 4 hours, and A/J = 7 hours
=> B = A/4 and J = a/7
B and J says how much area they can paint per hour.
When both of them work together, assume it takes x hours to finish the work
=> xB + xJ = A the total area painted
x(A+B) = x(A/4+A/7)=A
x (1/4+1/7)= 1 so x = 28/11
Jacob's answer explains it better, but there is an equation you can use.
Tt = 1/T1 + 1/T2
where Tt is total time, T1 is the first person's time, and T2 is the second person's time (this can be carried out as far as needed, such as by adding a 1/T3 term, and a 1/T4 term, etc.).
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To find out how long it takes to paint the house if Bill and John work together, we can use the concept of their combined work rates.
First, let's determine their individual work rates. We can calculate this by finding the inverse of the time taken for each person to complete the job.
Bill's work rate: 1 job / 4 hours = 1/4 job per hour
John's work rate: 1 job / 7 hours = 1/7 job per hour
Now, to find their combined work rate when they work together, we add their individual work rates:
Combined work rate: 1/4 + 1/7 = 11/28 job per hour
Finally, we can determine the time it takes for them to complete the job together by taking the reciprocal of their combined work rate:
Time taken when they work together: 1 / (11/28) = 28/11 hours
Therefore, it would take Bill and John approximately 2.54 hours, or 2 hours and 33 minutes, to paint the house together.