Question

Jake and Stewart are traveling in two separate cars to Rocky Point from their homes. They both leave at 6:30 a.m., but Stewart lives 12 miles closer to Rocky Point. Stewart's average speed is 70 miles per hour. Jake drives a little faster in hopes of catching up with Stewart, so his average speed is 78 miles per hour. What time will it be when Jake catches up with Stewart, and how far will they be from home when they meet? (Assume they don't cross time zones and that they are on the same road.)

A. 8:20 a.m.; 135 miles
B. 7:40 a.m.; 98 miles
C. 8:40 a.m.; 169 miles
D. 8:00 a.m.; 117 mile

Answer 1

Let's try making a function that describes each person's motion and then setting them equal - this should give us the time it takes. Speed is a function of time.
Jake: 78t
Stewart: 12+70t

Answer 2

Do you see why I added 12 to Stewart's function, and why their speeds are multiplied by t?

Answer 3

Setting them equal because the distance is equal, right?
78t = 70t +12
8t = 12
t= 12/8
t = 3/2
so it will take them an hour and a half to meet, right?

Answer 4

Add 1:30 to 6:30 am and get 8:00 am when they meet up

Answer 5

When we plug in our time, 3/2 hr into 78t or 70t+12 we should get distance :)

Answer 6

GREAT! THANKS!!!!!!

Answer 7

No problem :)