A private airplane leaves an airport and flies due east at 192 km/hr. Two hours later, a jet leaves the same airport and flies due east at 960 km/hr. How long after the jet leaves will it overtake the plane?

The answer is 0.5 hours.

A velocity (v) of an object is a distance (d) divided by time (t):

v = d : t ⇒ t = d : v

It is given:

v1 = 192 km/h

v2 = 960 km/h

t1 - t2 = 2h

We need to calculate t2.

Since they will travel the same distance before the jet overtakes the plane, we can say that d1 = d2 = d

Now, let's express t1 and t2:

t1 = d/192

t2 = d/960

Therefore: d/192 - d/960 = 2

The least common denominator is 960, so:

5d/960 - d/960 = 2

4d/960 = 2

4d = 2 · 960

4d = 1920

d = 1920 : 4 = 480 km

Now t2 = d/960 = 480/960 = 0.5 hours.