Jennifer rode her bike at 12 miles per hour for 4 hours, then put her bike down and began walking at 2 miles per hour. Thomas started walking at 4 miles per hour along the same path at the same time that Jennifer started biking. When he reached the bike, he began riding it at 12 miles per hour. How many hours will it have been since they started when Thomas catches up to Jennifer?
+116126 Let the time Jennifer walks = J
4 hrs * 12mph = 48 miles
The total distance she travels = 48 + 2J
So the total hrs she travels = 4 + J
The time it took Thomas to reach the bike is 48/ 4 = 12 hours
Let his time on the bike = T
So the distance he travels is 48 + 12T
And the time he travels = 12 + T
The time they travel is equal and so is the distance ....so...
4 + J = 12 + T (1)
48 + 12T = 48 + 2J ⇒ 12 T = 2J ⇒ 6T = J (2)
Sub (2) into (1)
4 + 6T = 12 + T
5T = 8
T = 8/5 = 1. 6 hrs
The total time to catch up to Jennofer = 12 + 1.6 = 13.6 hrs
Check
Distance Jennifer travels = 48 + J = 48 + 2*6(1.6) = 67.2 miles
Distance Thomas travels = 48 + 12 (1.6) = 67.2 miles
Jennifer has biked 12 * 4 = 48 miles while Thomas has walked 4 x 4 = 16 miles
it will take him 8 more hours to get to the bike at which time Jennifer will have walked 8 x 2= 16miles
their closing speed once T starts biking is 12 -2 = 10 m/hr 16miles will take 1.6 more hours
4 hours + 8 hours + 1.6 hours =13.6 hours from their start they will meet .
