Hi there. I have this Math Algebra Motion Problem and can't figure it out help?

Question

Bob and Susan leave Richmond traveling South at 60 mph. Rich and Jude follow 2 hours later at 80 mph. How long will Bob and Susan travel before Rich and Jude catch up?

Answer 1

Let x = time travelled by Bob and Susan

Let y = time travelled by Rich and Jude

y = x - 2 (because Rich and Jude left 2 hours later)

Find:

60x = 80y

Substitute y = x - 2 into 60x = 80y:

60x = 80(x - 2)

60x = 80x - 160

160 = 20x

8 = x

y = x - 2

y = 8 - 2

y = 6

Rich and Jude will catch up to Bob and Susan in 6 hours.

Answer 2

The key to these type of problems is to remember that distance equals velocity times time.

d = v * t

Bob and Susan,  d = 60 * t

Rich and Jude,  d = 80 * (t - 2),  t - 2 because R and J are 2 hours behind.

Since at catch up the distance is the same:

60 * t = 80 * (t - 2), solve for t

Answer 3

20 mph is the diff.

Bob has 60(2) = 120 mile head start

120/20 = 6 hrs