Strawberries?

Question

Al, Betty, and Carl can harvest a strawberry crop in 12 hours if they work together. If each person worked alone, Al could complete the job in 30 hours, and Carl would take twice as long as Betty. How long would it take Carl to do the job?

Please explain!!! :(

Answer 1

Let Al's rate be 1/30 of the job per hour.
Let Betty's rate be 2/C of the job per hour
Let Carl's rate be 1/C of the job per hour

1/30 + 2/C + 1/C = 1/12

1/30 + 3/C = 1/12

Multiply everything by 60 to get rid of denominators:
2 + 180/C = 5
180/C = 3
180 = 3C
C = 60

Carl takes 60 hours
Betty takes 30 hours
Al takes 30 hours

Answer 2

Here's how to do it:
First, we need to find a common standard.

So we decide to set each number equal to the capacity
PER HOUR.

The entire group would complete 1/12 of the job in one hour
and Al would complete the job in 30 hours.
So,
1/12(Everyone) = 1/30(Al) + X(carl) + 2X(betty)
Betty is 2x because she gets twice as much done as Carl in the same time. Careful, Carl takes twice as must TIME. Its easy to put the x and 2x in the wrong places.
x equals the fraction of the complete job per hour.

We change the denomiator to the least common multiple,which is 120 and add x and 2x, which equals 3x.

1/12 becomes 10/120
1/30 becomes 4/120

our new equation is :

10/120 = 4/120 + 3x
which becomes

6/120 = 3x x=2/120 = 1/60 ,
Carl completes 1/60 of the project by himself per hour,
which means he would take 60 hours.
The problem does not ask about Betty,
but if it did:
2 * 1/60 = 1/30 , Betty would take 30 hours.
Finally, we check our work:

does 1/12 = 1/30 + 1/60 + 1/30 ?
yes, it does.

Answer 3

Assuming all of them work at equal pace,
In 1 hour, Al can complete 1/30 of the job
In 1 hour, Betty can complete 1/x of the job
In 1 hour, Carl can complete 1/2x of the job
In 1 hour, all 3 together can complete 1/12 of the job

1/30 + 1/x + 1/2x = 1/12
Multiply throughout by 60x (Least Common Multiple of the four denominators),
2x +60 + 30 = 5x
...
x = 30

So, Carl would take 2(30) = 60 hours to do the job.

Answer 4

1 crop in 12 hours, a rate of 1/12
Al: 1/30
Betty: 1/t
Carl: 2(1/t)

1/30 + 1/t + 2/t = 1/12
1/30 + 3/t = 1/12
1 + 90/t = 5/2
90/t = 3/2
90/(3/2) = t
t = 60

Betty: 2/60 = 1/30
Carl: 1/60

It would take Carl 60 hours to do the job.

Answer 5

Al takes 30 hours
Carl takes 2x hours
Betty takes x hours

After 1 hour:
Al has completed 1/30 of the job
Carl has completed 1/2x of the job
Betty has completed 1/x of the job

They have completed
1/30 + 1/2x + 1/x
= (x + 15 + 30)/30x
= (x + 45)/30x

(x+45)/30x = 1/12
12(x+45) = 30x
12x + 540 = 30x
18x = 540
x = 30
2x = 60

Carl would require 60 hours to do the job alone.

Answer 6

60