Solve the word problem. lee can frame a cabin in 4 days less than ron. when they work together, they will do the job in 4 4/5 days. how long would each of them take to frame the cabin alone?

Step-by-step explanation:

Let L represent the time it takes Lee to frame the cabin. Then it takes L+4 days for Ron to frame the cabin. Working together, the framing time is ...

  L(L+4)/(L +(L+4)) = 4 4/5

Multiplying by 5(2L+4), we get

  5L(L +4) = 24(2L +4)

  5L^2 +20L = 48L +96 . . . . . eliminate parentheses

  5L^2 -28L -96 = 0 . . . . . . . . subtract 48L+96

  (5L +12)(L -8) = 0 . . . . . . . . . factor

The solution of interest is one that makes a factor be zero:

  L = 8

It takes Lee 8 days to frame the cabin and Ron 12 days when they each work alone.

For "working together" problems where rates are given as "time per job", it is usually useful to invert the numbers to give "jobs per time". Here, Lee can complete 1/L framing jobs per day, and Ron can complete 1/(L+4) framing jobs per day. Working together, they complete a total of ...

  1/L + 1/(L+4) = ((L+4) +(L))/(L(L+4)) . . . . framing jobs per day

Inverting that result gives the "days per job" when they work together:

  days per job = L(L+4)/(2L+4) . . . . . . the formula we used above

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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