The amount of time p people to paint d doors varies directly with the number of doors and inversely with the number of people. Four people can paint 10 doors in 2 hours How many people will take to paint 25 doors in 5 hours?

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Answer 1 · 2017-04-18T06:17:46

#4#

The first sentence tells us that the time #t# taken for #p# people to paint #d# doors can be described by a formula of the form:

#t = (kd)/p" "# ... (i)

for some constant #k#.

Multiplying both sides of this formula by #p/d# we find:

#(tp)/d = k#

In the second sentence, we are told that one set of values satisfying this formula has #t=2#, #p=4# and #d=10#.

So:

#k = (tp)/d = (2*4)/10 = 8/10 = 4/5#

Taking our formula (i) and multiplying both sides by #p/t#, we find:

#p = (kd)/t#

So substituting #k=4/5#, #d=25# and #t=5#, we find that the number of people required is:

#p = ((4/5)*25)/5 = 20/5 = 4#