SOLUTION: the amount of time it takes to paint a house varies inversly with the number of painters. if it takes 4 painters 40 hours how long would it take 10 painters? A.100 HOURS B.26 HOU

Algebra ->  Rate-of-work-word-problems -> SOLUTION: the amount of time it takes to paint a house varies inversly with the number of painters. if it takes 4 painters 40 hours how long would it take 10 painters? A.100 HOURS B.26 HOU      Log On


   

Question 550903: the amount of time it takes to paint a house varies inversly with the number of painters. if it takes 4 painters 40 hours how long would it take 10 painters?
A.100 HOURS B.26 HOURS C.20 HOURS D.16 HOURS ...... how did you get the answer?
Found 3 solutions by TutorDelphia, josmiceli, scott8148:
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
Inverse variation uses the formula
y=k/x
If 40=k/4
Than k=160
So our formula is Time=160/Painters
t=160/10
t=16 hrs

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
They want you to show the inverse relation
which is +p+=+k%2A%281%2Ft%29+
where
+p+ = number of painters
+t+ = hours it takes them to paint a house
+k+ = constant of proportionality
------------------------------
You have to find +k+
given:
+4+=+k%2A%281%2F40%29+
+160+=+k+
Now you can say:
+10+=+160%2A%281%2Ft%29+
+10t+=+160+
+t+=+16+
(D) 16 hours is the answer

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
it takes 160 painter-hours (like man-hours) to paint the house

4 * 40 = 10 * x