A cat chases a mouse, which has a 160 meters head start.For every 7 metes the mouse runs, the cat run 9 meters. How far must the car run to catch the mouse
Please I need solutions
both run for time t
cat runs d + 160 meters
cat speed= v
mouse speed = 7/9 v
so
7/9 v * t = d
v * t = d+160
t = 9 d / 7 v
v (9 d/7v) = d + 160
9d / 7 = d + 160
9 d= 7 d + 1120
2 d = 1120
d = 560
so
d + 160 = 720 = cat distance
for every 9 m the cat runs , he closes the distance to the mouse by 2 m
160 m / 2 m = 80 ... "steps" to catch mouse
9 m * 80 = ?
LOL --- Thanks R_scott. That is much easier than my way.
160/2 = answer because the cat is running 2 more meters that the mouse at a time
To calculate the distance the cat must run to catch the mouse, we need to determine the relative speed between the cat and the mouse.
We know that for every 7 meters the mouse runs, the cat runs 9 meters. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 1 in this case. Therefore, the simplified ratio is 7:9.
Now, let's calculate the distance the cat runs when the mouse has covered 160 meters. To do this, we'll set up a proportion:
7 meters (mouse's distance) : 9 meters (cat's distance) = 160 meters (mouse's head start) : x meters (cat's distance)
Using cross-multiplication, we can solve for x:
7x = 9 * 160
7x = 1440
x = 1440 / 7
x ≈ 205.71
Therefore, the cat must run approximately 205.71 meters to catch the mouse.