SOLUTION: Would you be so kind to help me with following problem. Typist faund out that she could complete her typing work 3 hours earlier if she would speed up her typing and type 2 pages

Question 876246: Would you be so kind to help me with following problem.
Typist faund out that she could complete her typing work 3 hours earlier if she would speed up her typing and type 2 pages more each hour. If she could type 4 pages more each hour, her work could be completed 5 hours earlier. How many pages she must type and in what time?
Thanks,
Niko
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let x pages /hour be the rate to finish in time
let t be the normal time required
I condition
(x+2)(t-3) =xt
xt-3x+2t-6=xt
3x-2t=-6........................(1)

II condition
(x+4)(t-5)=xt
xt-5x+4t-20=xt
5x-4t=-20
.....................................(2)
solve (1) & (2)
3 x -2 t = -6 .............1

5 x -4 t = -20 .............2
Eliminate y
multiply (1)by -2
Multiply (2) by 1
-6 x 4 t = 12
5 x -4 t = -20
Add the two equations
-1 x = -8
/ -1
x = 8
plug value of x in (1)
3 x -2 t = -6
24 -2 t = -6
-2 t = -6 -24
-2 t = -30
t = 15
8 pages /hour
15 hours actual time
m.ananth@hotmail.ca

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