Tom can plow his field in 35 hours. Brad can plow his field, which is 75% larger than Toms, in 50 hours. Karl can plow his field, which is 2.5 times larger than Brads, in 100 hours. If the three men worked together, how long would it take them to plow all 3 fields? Thank you for help.

Guest Jul 7, 2018

Let the size of Tom's field = F, then:
The size of Brad's field =1.75F, and:
The size of Karl's field =2.5 x 1.75F = 4.375F
Tom plows: (1/35)F in 1 hour, and:
Brad plows:(1.75/50)F in 1 hour, and:
Karl plows:(4.375/100)F in 1 hour, then:
All 3 men working together can plow the 3 fields in H hours:
[F + 1.75F + 4.375F] / [(1/35)F +(1.75/50)F + (4.375/100)F] =H, solve for H
     7.125F / 0.107321428571....F = H
H = 66.38935 hours =~66 hours and 23.361 minutes.

Guest Jul 8, 2018

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