1. d = r  t
1) Two planes take off at the same time, departing in separate directions. One plane travels 3 times as fast as the other plane. After 3 hours, they are 1620 miles apart. What is the average speed of each plane?
plane 1 d + plane 2 d = total d
Make a table
3r + 9r = 1620
12r = 1620
rate x time = distance 12 12 r
Plane 1 3 3r
r = 135 3r
Plane 2 3 9r
Plane 1 = 135 mph
P 1 = 3r
P 2 = 9r
Plane 2 = 3(135)
= 405 mph
1620 miles

2. It will be ½ hour until they meet. 4.5 miles
2) Rob and Joe live 4.5 miles apart. Joe leaves his house walking at 3 mph. However, at the same time Rob runs from his house at 6 mph. The are heading toward each other. How long will it be until they meet?
rate x time = distance
Rob d + Joe d = total d 6
Rob t 6t
3t + 6t = 4.5 3 t 3t
Joe
9t = 4.5 9 9
t = 0.5
Joe = 3t
Rob = 6t
It will be ½ hour until they meet.
4.5 miles

3. 3) A train leaves the station averaging 40 mph
3) A train leaves the station averaging 40 mph. Four hours later a second train leaves a stations 440 miles away traveling toward the first train on an adjacent track at a rate of 60 mph. How long will it be until they pass each other?
A d + B d = total d
rate x time = distance
40t + 60(t – 4) = 440 40
Train A t
40t
40t + 60t – 240 = 440 60
t – 4
60(t-4)
Train B
100t – 240 = 440
+240
+240
B = 60(t-4)
A = 40t
100t = 680
100
100
440 miles
t = 6.8 hours
Train A = 6 hrs. 48 min.
Train B = 2 hrs. 48 min.

4. 4) Sandi’s family left for vacation at the beach, driving an average of 55 mph. On the return trip they were only able to average 45 mph due to road construction. If the return trip took 2 hours longer, how far from the beach does Sandi’s family live?
To d = From d
rate x time = distance
55t = 45(t + 2) 55
To Beach t
55t
55t = 45t + 90
-45t
-45t 45
t + 2
45(t+2)
From Beach
10t = 90 10 10
To Beach = 55t
t = 9
From Beach = 45(t+2)
Distance = 55  9
= 495 miles
Distances are the same!