Linda headed east at 20 miles per hour on her bicycle at 9am

Linda headed east at 20 miles per hour on her bicycle at 9am. Three hours later Shana headed west from the same place walking at 6 miles per hour. What time was it when they were 164 miles apart?

Solution

Let t = time (in hrs) Linda rode her bike
Then (t-3) = Shana\'s time walking
:
Write a distance equation: dist = speed * time
:
Linda\'s dist + Shana\'s dist = 164
20t + 6(t-3) = 164
20t + 6t - 18 = 164
26t = 164 + 18
26t = 182
t = 182/26
t = 7 hrs, Linda is on the road
:
Time: 9 AM + 7 hrs = 4 PM, they will be 162 miles apart
:
Check using Linda\'s and Shana\'s distances:
20(7) + 6(7-3) =
140 + 24 = 164 mi