Topic: S can paint a house in 4hrs & J can paint the same house in 6hrs, how long will it take if painted together?
July 19, 2019 / By Cheyenne Question:
I was taking a practice aptitude test to get myself prepared for the real one and didn't really get stuck on anything except this question. I know the answer (2hrs 24mins), but for some reason I still can't figure out how to solve a problem like this. Please, can anyone solve this properly and explain it to me as ridiculously dumbed down as tolerable? I would greatly appreciate the help... it's driving me nuts...I can usually hold my own when it comes to math problems but now my confidence is gone completely. I need help! Oh and I had to break the question down to get it to fit. Here it is in its entirety: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
AHH HA HA! Okay, nice! I get it now... THANKS!!!
Math-magicianry... It always seems so simple after you find out how it's done!
Aspen | 8 days ago
I used to have trouble with these as well... What I do is take the numbers and turn them in to rates.
J paints 1 house in 6hrs, that means he paints 1house/6hrs or 1/6 houses/hr
S paints 1 house in 4hrs, meaning that she paints 1house/4hrs or 1/4 houses/hr
Now try using the rates to write an expression...
For J, (1/6)(X) = 1house, X = 6hrs
For S, (1/4)(X) = 1house, X = 4hrs
Now you want to know how long it takes them to paint 1 house together.
For J and S, (1/6)(X) + (1/4)(X) = 1house
Simplify (10/24)(X) = 1house
X = 24/10hrs or 2.4hrs or 2hrs and 24mins
Go the basics, the UNITS.
If S paint in 4 hs, 1/4 of the house is made in one hour
If J paint in 6 hs, 1/6 of the house is made in one hour
So in ONE hour they do together 1/4 + 1/6 = 5/12 of the house
Now apply a rule of three:
1 Hr --- 5/12
x Hr --- 1
Solution: 12/5 hs. to finish the house = 2.4 hours (0.4 hs = 24 min)