Thread: Need help with a rate/time problem

1. Need help with a rate/time problem

Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

So far this is what I got:

Rate Distance Time
Cathies 3x 1 1/3x
Beth 2x 1 1/2x
Abbie x 1 1/x

I then did (1/2x)+(1/3x)+(1/x)=1

Can someone explain to me where I keep going wrong? Thanks

2. Originally Posted by coolieman
Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

So far this is what I got:

Rate Distance Time
Cathies 3x 1 1/3x
Beth 2x 1 1/2x
Abbie x 1 1/x

I then did (1/2x)+(1/3x)+(1/x)=1

Can someone explain to me where I keep going wrong? Thanks
here only abbie can do painting in 50 nminutes.
that is let abbie=x
beth=2x
cathies=3x
so x+2x+3x=6x
6x can paint in 60min
x=10minutes
60-10=50minutes.

3. Originally Posted by coolieman
Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all 3 working together, how long would it take Abbie if she works alone?

So far this is what I got:

Rate Distance Time
Cathies 3x 1 1/3x
Beth 2x 1 1/2x
Abbie x 1 1/x

I then did (1/2x)+(1/3x)+(1/x)=1

Can someone explain to me where I keep going wrong? Thanks
Umm, you used the formula, Distance = Rate * Time here. Very good.
I use, task = rate *time.

Abbie paints twice as fast as Beth and three times as fast as Cathie.
Let A = rate of Abbie painting alone
And B = rate of Beth painting alone
And C = rate of Cathie painting alone

So,
A = 2B -----(i)
so,
B = A/2

A = 3C ----(ii)
so,
C = A/3

If it takes them 60 min to paint a living room with all 3 working together,
Rate *time = distance
(A +B +C)(60min) = 1 complete job
(A +A/2 +A/3)(60) = 1
60A +30A +20A = 1
110A = 1
A = 1/110 job/min -----rate of Abbie working alone.

It means Abbie can finish the job, working alone, in 110 minutes. ----answer.

Check,
Distance = Rate *Time
1 = A *110
A = 1/110 -------------OK.

Check,
A = 1/110
B = A/2 = 1/220
C = A/3 = 1/330

Distance = Rate *time
1 =? (A +B +C)(60)
1 =? (1/110 +1/220 +1/330)(60)
1 =? [(6 +3 +2)/660](60)
1 =? [11/660](60)
1 =? 660/660
1 =? 1
Yes, so, OK.