SOLUTION: Ben can paint a fence in 3hrs and billy takes 4hrs. How long will it take them painting together?

Question 386918: Ben can paint a fence in 3hrs and billy takes 4hrs. How long will it take them painting together?
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
we have : 3h=L/v_ben, and 4h=L/v_bil, where L is the length, v_x is the painting speed of x.
If they paint together : L_ben+L_bil=L=t(v_ben+v_bil)=t(L/3+L/4)

hence the time needed is : t = L/(L/3+L/4)=1/(1/3+/4)=12/7 hours, or 1.71 hours, which is half of the harmonic mean. It's parallel working, so the same formula as in electronics with resistance.

check : with the speed of painting : 12/7*L/3+12/7*L/4=L*12/7*(1/3+1/4)=L*12/7*7/12=L, which is the total length to be paint.

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