Word Problem Help

Question

tito, working alone, can complete a task in 18 hours. Ronnie, working alone, can complete the same task in 12 hours. Ronnie begins working on the task alone. Four hours later, Tito joins Ronnie, and they complete the task working together. How long did Ronnie work on the task?

Answer 1

Tito completes the task in 18 hours

Tito does 1/18 of the job in one hour

Ronnie completes the task in 12 hours

Ronnie does 1/12 of the job in one hour

x=# of hours they work together

x+4=# of hours Ronnie works altogether (Ronnie begins working alone for 4 hours)

(1/18)x+(1/12)(x+4)=1 (job finished)

multiply both sides by 36 (LCM of 12 and 18)

36(1/18)(x)+36(1/12)(x+4)=36(1)

2x+3(x+4)=36

2x+3x+12=36

5x+12=36

5x=36-12

5x=24

x=24/5

x=4.8 hours that they work together

4.8+4=8.8 hours is the amount of time that Ronnie worked

 

Answer 2

Hi Frank,

 

So if Tito can do the task in 18 hours, how much can he do in 1 hour

 

1/18

 

and if Ronnie can do the task in 12 hours, how much can he do in 1 hour

 

1/12

 

now Ronnie works alone for 4 hours, so Ronnie complete

 

4*1/12 = 1/3 of the job

 

and there is 2/3 of the job left for Tito and Ronnie to complete when they work togethe

 

let x = the hours is takes them

 

x(1/18) + x(1/12) = 2/3

 

multiply both sides of the equation by 36 which is the least common denominator

 

2x + 3x = 24

 

5x = 24

x = 4.8 hrs

 

check it

 

4.8(1/18) + 4.8(1/12) = 2/3

 

.8/3 + 1.2/3 = 2/3

2/3 = 2/3  and it all checks out

 

Hope this helps