Father can paint the fence of their garden in 2 hours working alone. His son, alone, can paint the fence in 3.5 hours. How long will it take them to paint the fence together?
Father's rate = job/2 hrs
son's rate = job/3.5 hrs
combined rate = job/2 + job/3.5 = job/2 + 2job/7
= (7job + 4job)/14 hrs = 11job/14 hrs
time together = job รท (11job/14 hrs)
= 14/11 hrs or appr 1 hour and 16 minutes
To find out how long it will take them to paint the fence together, we need to calculate their combined painting rate.
Let's start by determining how much of the fence each person can paint per hour working alone.
Father can paint the entire fence in 2 hours, so his painting rate is 1 fence / 2 hours = 1/2 fence per hour.
Similarly, the son can paint the fence in 3.5 hours, which means his painting rate is 1 fence / 3.5 hours = 2/7 fence per hour.
To determine their combined painting rate, we add their individual rates together:
1/2 fence per hour + 2/7 fence per hour = 7/14 fence per hour + 4/14 fence per hour = 11/14 fence per hour.
Now that we know their combined painting rate, we can calculate the time it will take them to paint the fence together:
Time = 1 fence / Combined rate
Time = 1 / (11/14)
Time = 14/11
Therefore, it will take them approximately 1 hour and 16 minutes (14/11 hours) to paint the fence together.
they each paint a fraction of the fence based on their own rate
... the fractions sum to one (the whole fence)
t / 3.5 + t / 2 = 1
multiplying by 7 ... 2 t + 3.5 t = 7 ... 5.5 t = 7
T1 = 2 h, T2 = 3.5 h.
T = T1*T2/(T1+T2) = 2*3.5/(2+3.5) = 14/11 = 1.37 h.