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?

Answer 1

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

Answer 2

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 ÷ (11job/14 hrs)
= 14/11 hrs or appr 1 hour and 16 minutes

Answer 3

T1 = 2 h, T2 = 3.5 h.
T = T1*T2/(T1+T2) = 2*3.5/(2+3.5) = 14/11 = 1.37 h.