The time to do a piece of work is inversely proportional to the number of men employed. If it takes 4 men to do a piece of work in 5days,how long will it take 25 men?

2 Answers
Jim G.
Jul 6, 2018

#19" hours and "12" minutes"#

Explanation:

#"let t represent time and n the number of men"#

#"the initial statement is "tprop1/n#

#"to convert to an equation multiply by k the constant"#
#"of variation"#

#t=kxx1/n=k/n#

#"to find k use the given condition"#

#t=5" when "n=4#

#t=k/nrArrk=tn=5xx4=20#

#"equation is "t=20/n#

#"when "n=25#

#t=20/25=4/5" day"=19.2" hours"#

#color(white)(xxxxxxxxxxxx)=19" hours and "12" minutes"#

Hriman
Jul 6, 2018

Let #t# be time, #m# be the number of men, and #k# the constant of variation

Inverse variation can be modeled by:
#tm=k#
Given that in 5 days, 4 men can complete work:
#(5)(4)=k#

#k=20#

To solve for time, when 25 men work:
#t=k/m#

#t=20/25#

#t=4/5#

#t= 4/5" day" or 19" hrs" and 12" mins"#

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