274 algebra De mystif ieD

Jim needs 24 minutes to wash the car by himself.

Kellie can mow the campus yard in 212 hours. When Bobby helps, they can

mow the yard in 121 hours. How long would Bobby need to mow the yard by

himself?

Let t represent the number of hours Bobby needs to mow the yard himself.

Kellie’s time is 212 or 25. Then her rate is^12

(^525)
=.
The together time is 121 or^32 , so the together rate is^12
(^323)
=.
Worker Quantity Rate Time
Kellie 1 2/5^212
Bobby 1 1/t t
Together 1 2/3^112
The equation to solve is^2
5
  + ^1 = ^2
3
.
t
The LCD is 15t.
2
5
12
3
15 2
5
1 15 2
3
15 2
5
1
+=

• 
  

  
  
  
  

  
  

  
  
  
  
  
  
  
  

  
  


• 
  

  t
  t
  t
  t
  t 55 1 10
  61510
  66
  15 4
  15
  4
  t
  t
  t
  tt
  tt
  t
  t
  
  
  
  

  
  

  +=
  −−

  
  

  =
  Bobby needs^15
  4
   =  334 hours or 3 hours 45 minutes to mow the yard by
  himself.
  PRACTICE

  
  

1. Sherry and Denise together can mow a yard in 20 minutes. Alone, Denise
   can mow the yard in 30 minutes. How long would Sherry need to mow
   the yard by herself?


2. Together, Ben and Brandon can split a pile of wood in 2 hours. If Ben
   could split the same pile of wood in 3 hours, how long would it take
   Brandon to split the pile alone?

PRACTICE

1. Sherry and Denise together can mow a yard in 20 minutes. Alone, Denise