Question

A cheetah can run at a maximum speed 107 km/h and a gazelle can run at a maximum speed of 71.8 km/h. If both animals are running at full speed, with the gazelle 95.6 m ahead, how long before the cheetah catches its prey? Answer in units of s.

Answer 1

9.8 seconds

Step-by-step explanation:

Let's start by changing the speeds of both animals into meters per second:

107 km/h = 107000 m/3600s = 29.72 m/s

71.8 km/h = 71800 m/3600s = 19.94 m/s

The distance covered equation for the cheetah is:

Dc = 29.72 t

The distance covered equation for the gazelle considering as origin the cheetah's starting location, is:

Dg = 95.6 + 19.94 t

We make both equations equal at the time (t) the cheetah catches with the gazelle:

Dc =Dg

29.72 t = 95.6 + 19.94 t

solve for "t":

29.72 t - 19.94 t = 95.6

9.78 t = 95.6

t = 95.6 / 9.78

t = 9.775 seconds

We can approximate it to 9.8 seconds