# Anthony left home 2 hours before Greg. Both boys were traveling to see their grandmother in New York. Anthony drove at 50 mph and greg drove 65 mph. how long did it take greg to catch up with Anthony?

May 31, 2015

Let $t$ represent time in hours, using $t = 0$ to represent the time Greg set out.

At time $t \ge 0$ Anthony will have travelled $50 \left(t + 2\right)$ miles and Greg $65 t$ miles.

Greg will catch up with Anthony when $65 t = 50 \left(t + 2\right)$

$65 t = 50 \left(t + 2\right) = 50 t + 100$

Subtract $50 t$ from both ends to get:

$15 t = 100$

Divide both sides by $15$ to get

$t = \frac{100}{15} = \frac{90}{15} + \frac{10}{15} = 6 + \frac{2}{3} = 6$ hours, $40$ minutes.