Steve leaves Nashville to visit his cousin David in Napa 80

Steve leaves Nashville to visit his cousin David in Napa 80 miles away. He travels at an average speed of 50 m/hr. Half an hour later, David leaves to visit Steve traveling at an average speed of 60 m/hr. How long after David leaves will they meet?

Solution

When they do meet they will have traveled a total of 80 mi
:
Let t = David\'s time
Then (t+.5) = Steve\'s time (he left a half hour earlier)
:
Distance = speed * time
Steve\'s distance: 50(t+.5)
David\'s distance: 60t
:
Steve\'s distance + David\'s distance = 80
50(t+.5) + 60t = 80
:
50t + 25 + 60t = 80
110t = 80 - 25
110t = 55
t = 55/110
t = .5 or half an hour
:
:
Check our solution
Steve would be driving for 1 hr and david for a half hour:
(50 * 1) + (60 * .5) = 80