The slow cat put 10 mice per minute in his basket.
......4 minutes later......
The fast cat put 20 mice per minute in his basket.
(The slow cat: cyan line)
(The fast cat: magenta line)
y=10*x in minutes
y=20*(x-4) in minutes
The 10*x or the 20*x are also named: "the slope of the line".
In this grid, each vertical space means 10 mice; and each horizontal space, means 1 minute (60 seconds)
SOLUTIONS:
In the minute 8, (Minute 4 for the fast cat [he awake at minute 4]):
The slow cat has 80 mice in his basket (8 min*10 mice/minute)
The fast cat has 80 mice in his basket (4 min*20 mice/minute)
If you wish to solve this problem without graphics, this can be the way:
Slow cat: 10 mice/minute; Fast cat: 20 mice/minute.
They will have the same number of mice in the 2 baskets.
We must equal the number of mice in both baskets:
10*x=20*(x-4)
10*x=20*x-80
10*x+80=20*x-80+80
10*x+80=20*x
10*x-10*x+80=20*x-10*x
80=10*x
x=80/10
x=8 minutes
The same in seconds:
10 mice/minute = 10/60 = 0.1666666 mice/second
20 mice/minute = 20/60 = 0.3333333 mice/second
4 minutes=240 seconds
0.1666666*x=0.3333333*(x-240)
0.1666666*x=0.3333333*x-80
80=0.1666666*x
x=80/0.1666666
x=480 seconds = 8 minutes
