Jake can cut and split a cord of firewood in 6 fewer hr(s) than Suzie can. When they work together, it takes them 4 hr(s). How long would it take each of them to do the job alone?

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Answer 1 · 2018-06-09T14:30:25

It takes 12 hours for Suzie and 6 for Jake.

Let #r# be Jake's rate, cords per hour, and #s# Suzie's rate.

Jake can cut and split a cord of firewood in 6 fewer hours than Suzie can. It takes Jake #1/r#hours to split a cord, Suzie #1/s.#

# 1/r = 1/s - 6#

When they work together, it takes them 4 hours.

#1/{r+s} = 4 #

#6 = 1/s - 1/r = {r-s}/{rs}#

#6rs = r-s#

# 1 = 4(r + s) #

# r = 1/4 -s #

#6( 1/4 -s )s = ( 1/4 -s ) -s#

#6 s - 24 s^2 = 1-8s#

#24s^2-14s + 1 = 0#

#(2s-1)(12s-1)=0#

#s=1/2 or s=1/12#

Only the second gives a positive #r#.

# 1/r = 1/s - 6 = 12-6=6#

#r = 1/6#

Jake can cut and split a cord of firewood in 6 fewer​ hr(s) than Suzie can. When they work​ together, it takes them 4 ​hr(s). How long would it take each of them to do the job​ alone?