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.
7+4= 11/2 is equal to 9 and 1 half hours.
Oh heavens, it takes them longer working together Lu ????
Bill paints 1/4 house per hour
John paints 1/7 house per hour
so together they paint
1/4 + 1/ 7 = 7/28 + 4/28 = 11/28 houses per hour
which is 28 /11 hours/house
or around 2.55 hours
or 2 hours and 33 minutes
To find out how long it takes for Bill and John to paint the house together, we can use the concept of work rates.
Let's first calculate their individual work rates.
Bill can paint 1 house in 4 hours, so his work rate is 1 house / 4 hours = 1/4 houses per hour.
John can paint 1 house in 7 hours, so his work rate is 1 house / 7 hours = 1/7 houses per hour.
To find their combined work rate, we add their individual work rates together:
Combined work rate = Bill's work rate + John's work rate
Combined work rate = 1/4 + 1/7
To add these fractions, we need to find a common denominator:
Combined work rate = 7/28 + 4/28
Combined work rate = 11/28 houses per hour
So, when working together, Bill and John can paint a combined rate of 11/28 houses per hour.
To find how long it will take them to paint the house together, we can invert the combined work rate:
Time = 1 / Combined work rate
Time = 1 / (11/28)
When we divide 1 by 11/28, we can multiply 1 by the reciprocal of 11/28:
Time = 1 * (28/11)
Time = 28/11
Therefore, when Bill and John work together, it will take them approximately 2.54 hours (or 2 hours and 33 minutes) to paint the house.