Question 963453: A cat runs 3 times as fast as a mouse. If a mouse runs at 2 meters per second and is 12 m from a cat, the mouse will be caught in _____ seconds.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the rate of the mouse is 2 meters per second, then the rate of the cat is 6 meters per second since the cat runs 3 times as fast as the mouse.
the cat is 12 meters from the mouse.
the cat starts chasing the mouse.
the cat has to close the distance between the cat and the mouse.
if the distance the mouse runs is x meters, then the distance the cat has to run is x + 12 meters.
the time that both the cat and the mouse run is the same.
the basic formula is R * T = D
for the mouse, this formula becomes 2 * T = D
for the cat, this formula becomes 6 * T = D + 12
solve both of these formulas for T to get:
T = D/2 for the mouse.
T = (D + 12)/6 for the cat.
since both expressions on the right side of the equations are equal to T, the expressions can be set equal to each other to get:
D/2 = (D+12)/6
solve for D to get D = 6.
that means that the mouse has run 6 meters and the cat has run 18 meters, at which point in time the cat has caught the mouse.
let's see if that holds true.
the mouse runs at 2 meters per second for a time of T and runs 6 meters.
this means that the mouse has run for 3 seconds because 2 meters per second * 3 seconds is equal to 6 meters.
in the same time, the cat has run 6 meters per second * 3 seconds equals 18 meters.
Since the mouse was 12 meters away from the cat to start with, the cat has caught up with the mouse in 3 seconds.
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