Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 401

EXAMPLE
Together John and Michael can paint a wall in 18 minutes. Alone John
needs 15 minutes more to paint the wall than Michael needs. How much
time does each John and Michael need to paint the wall by himself?

Let t represent the number of minutes Michael needs to paint the wall.
Then t + 15 represents the number of minutes John needs to paint the
wall.

Worker Quantity Rate Time

Michael (^11) t^ t
John (^1) t+^115 t + 15
Together 1 181 18
The equation to solve is^11
15
1
tt 18
+   .
+ 
=  The LCD is 18t(t+ 15).
11
15
1
18
18 15 1 18 15 1
15
18
tt
tt
t
tt
t
tt

• 
  


• 
  

  =
  +⋅++⋅

  
  


• 
  

  () () =+( 115 1
  18
  18 15 18 15
  18 270 18 15
  3
  2
  )
  () ()
  ⋅
  ++=+
  ++=+
  tttt
  tttt
  66 270 15
  021 270
  0309
  2
  2
  ttt
  tt
  tt
  +=+
  =− −
  =−()()+
  t− 30 = 0 t+ 9 = 0 (This does not lead to solution.)
  t = 30
  Michael needs 30 minutes to paint the wall by himself and John needs
  30 + 15 = 45 minutes.
  EXAMPLE
  Together John and Michael can paint a wall in 18 minutes. Alone John
  needs 15 minutes more to paint the wall than Michael needs. How much
  time does each John and Michael need to paint the wall by himself?
  EXAMPLE
  Together John and Michael can paint a wall in 18 minutes. Alone John