SOLUTION: I'm really stuck with figuring this story problem can you help? it goes like this:WORKING ALONE, JAN COULD PAINT A CERTAIN ROOM IN 8 HOURS. WADE WORKING ALONE, COULD PAINT THE SAME

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I'm really stuck with figuring this story problem can you help? it goes like this:WORKING ALONE, JAN COULD PAINT A CERTAIN ROOM IN 8 HOURS. WADE WORKING ALONE, COULD PAINT THE SAME      Log On


   

Question 173461: I'm really stuck with figuring this story problem can you help? it goes like this:WORKING ALONE, JAN COULD PAINT A CERTAIN ROOM IN 8 HOURS. WADE WORKING ALONE, COULD PAINT THE SAME ROOM IN 10 HOURS.HOW LONG WOULD IT TAKE JAN AND WADE TOGEATHER TO PAINT THE ROOM?
Found 3 solutions by solver91311, Mathtut, ptaylor:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
(Stop using all CAPS -- it is the electronic equivalent of shouting, therefore both rude and annoying)

If Jan can paint a room in 8 hours, then she can paint 1%2F8 of a room in 1 hour.

Likewise, Wade can paint 1%2F10 of the same room in 1 hour.

In one hour, working together, Jan and Wade can paint 1%2F8%2B1%2F10=5%2F40%2B4%2F40=9%2F40 of the room in 1 hour.

Therefore they can paint the entire room in 40%2F9 hours. Not quite four and one-half hours. I'll leave it to you to figure out the hours, minutes, and seconds represented by 40%2F9 hours.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
Jan's rate is 1/8 of job per hour and Wade's rate is 1/10 of the job per hour.
:
together %281%2F8%2B1%2F10%29%28t%29=1(job)
:
%2810%2B8%29%28t%29%2F80=1
:
18t=80
:
highlight%28t=80%2F18=40%2F9%29hours to paint the room together

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes Jan and Wade together to paint the room
Together they paint at the rate of 1/x room per hour
Jan paints at the rate of 1/8 room per hour
Wade paints at the rate of 1/10 room per hour
Together they paint at the rate of 1/8 + 1/10=5/40 + 4/40=9/40 room per hour
So, our equation to solve is:
(9/40)x=1 (1 room that is) multiply each side by 40
9x=40 divide each side by 9
x=4 4/9 hours to paint the room with both working together
Another way:
1/x = 9/40 multiply each side by 40x
40=9x
x=40/9 hours
CK
(1/8)*(40/9)+ (1/10)*(40/9)=1 (room)
5/9 +4/9=1
9/9=1
1=1
Does this help?----ptaylor