# 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. So how long did it take greg to catch up with Anthony?

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. So how long did it take greg to catch up with Anthony?
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kregde84
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(t+2) miles and Greg 65t miles.
Greg will catch up with Anthony when 65t=50(t+2)
65t=50(t+2)=50t+100
Subtract 50t from both ends to get:
15t=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.