Rates P6

A piece of pasture grows at a constant rate every day. 200 sheep will eat up the grass  in 100 days. 150 sheep will eat up the grass in 150 days. How many days does it take for 100 sheep to eat up the grass?


Number      Number      Pasture  
of sheep      of days
--------------------------------------------------------------------
200              100           S  +  100 u
200                1             1/100 S + 1 u

150              150           S + 150 u
150                1            1/150 S+ 1 u

50                  1            (1/100 - 1/150) S = 1/300 S
50                 100         1/3 S
150               100         S  

50                 100         100 u

1/3 S --> 100 u
S --> 300 u

100               x              300 u + x u

100               1              1/150 S = 1/150 x 300 u
                                                  = 2 u
100               x               2 x u

2 x u --> 300 u + x u
x u --> 300 u
x --> 300 days

100 sheep will take 300 days to eat the grass.