Your friend is traveling at a constant 30.0m/s and has a 1600m head start. How many minutes will it take you to catch them if you are traveling at a constant 50.0m/s?

Nov 9, 2015

80 seconds

Explanation:

By defining $t$ as the time it will take to you and your friend to be in the same position $x$; ${x}_{0}$ is the starting position and using the equation of motion $x = {x}_{0} + v t$ you have:
$x = 1600 + 30 \cdot t$
$x = 0 + 50 \cdot t$
Since you want the moment when both are in the same position, that is the same $x$, you make both equations equal.
$1600 + 30 \cdot t = 50 \cdot t$
And solving for $t$ to know the time:
$t = \frac{1600 m}{50 \frac{m}{s} - 30 \frac{m}{s}} = \frac{1600 m}{20 \frac{m}{s}} = 80 s$