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.