Question

A mouse and a cat start 60 yards apart. At t=0, the cat begins chasing the mouse, running towards it at 4 yards/second, while the mouse begins running away from the cat at 3 yards/second. To find when the cat catches the mouse, you need to solve the equation (Enter an equation in t ) seconds. The cat will catch up with mouse after

Answer 1

The cat will catch the mouse after 8.57 seconds by setting up an equation based on their relative speeds and initial distance, resulting in t = 60 / 7 seconds.

Step-by-step explanation:

To find when the cat catches the mouse, we can set up an equation based on their relative speeds and the initial distance between them. At the beginning, they are 60 yards apart. The cat's speed is 4 yards/second and the mouse's speed is 3 yards/second. Since they are moving towards each other, we can consider their relative speed. The relative speed is the speed of the cat plus the speed of the mouse, because the mouse is moving away from the cat.

The equation for the time t when the cat catches the mouse can be set up as:

60 = (4 + 3) * t

This equation is based on the formula distance = speed * time. Plugging the values in we get:

60 = 7t

To find t, we divide both sides of the equation by 7:

t = 60 / 7 seconds

So, the cat will catch up with the mouse after 8.57 seconds.