The first number is 20, the second is 22, and the third is 24. The sum of the three even consecutive numbers is 66.

1. A train leaves the station at 6:00pm traveling west at 80 mi/h. On a
parallel track, a second train leaves the station 3 hours later traveling
west at 100 mi/h. At what time will the second train catch up with the
first?
Rate Time Distance
In miles/hour in hours in miles
Train 1 80 t 80t
Train 2
100 t-3 100 (t – 3)
80t = 100( t – 3)
80t = 100t – 300
-100t -100t The first train left at 6:00 pm and 15
hours later the second train caught
-20t = - 300 up at 9:00 am.
-20 -20
t = 15 hours

2. It takes 1 hour longer to fly to St. Paul at 200 mi/h than it does to return
250 mi/h. How far away is St. Paul?
Rate Time Distance
in miles/hour in hours In miles
Going there 200 t+1 200(t + 1)
Returning 250 t 250t
200(t + 1) = 250t 200( 4 + 1) =
200(5) = 1000 miles
200t + 200 = 250t
-200t -200t OR 250(4) = 1000 miles
200 = 50t St. Paul is 1,000 miles away.
50 50
t = 4 hours

3. On his way to work from home, your uncle averaged only 20 miles per hour.
On his drive home, he averaged 40 miles per hour. If the total travel time was
1.5 hours, how long did it take him to drive to work?
Rate Time Distance
Home to work 20 t 20t
Work to home 40 1.5 - t 40( 1.5 – t)
20t = 40( 1.5 – t)
20t = 60 – 40t
+40t +40t It took him 1 hour to drive to work.
60t = 60
t = 1 hours

4. Jane and Peter leave their home traveling in opposite directions on a straight
road. Peter drives 15 mi/h faster then Jane. After 3 hours, they are 225 miles
apart. Find Peter’s rate and Jane’s rate.
Rate Time Distance
Jane
r 3 3r
Peter 3( r + 15)
r + 15 3
3r + 3( r + 15) = 225
3r + 3r + 45 = 225
Jane was driving 30 miles/hour and
6r + 45 = 225 Peter was driving 45 miles/hour.
-45 -45
6r = 180
r = 30 miles/hour

5. Sarah and John Leave Perryville traveling in opposite directions on a straight
road. Sarah drives 12 miles per hour faster than John. After 2 hours, they are
176 miles apart. Find Sarah and John’s speeds.
Rate Time Distance
Sarah r + 12 2 2( r +12)
John
r 2 2r
2(r+12) + 2r = 176
2r + 24 + 2r = 176
John’s speed is 38 mils per hour and Sarah’s
4r + 24 = 176 is 50 miles per hour.
-24 -24
4r = 152
r = 38 miles/hour

6. In general…
• Define your variable to represent your
unknown and use this to define other
quantities
• There are 3 kinds of r(t)=d problems
– Same direction
– Opposite Direction
– Round trip

7. The width of a rectangle is 3 inches less than its length. The perimeter is 26
inches. What is the width of the rectangle?
L-3
L
Let L = length and Let W = L- 3 Perimeter = 2L + 2W
26 = 2L + 2( L - 3)
26 = 2L + 2L -6
26 = 4L - 6 So the width of the
+6 +6 rectangle is 5 inches long.
32 = 4L
4 4
L = 8 inches

8. The sum of 3 even consecutive numbers is 66. Find the 3 numbers.
Let n = the first number
Let n + 2 = the second number 20, 22, 24
Let n + 4 = the third number
n + n + 2 + n + 4 = 66
3n + 6 = 66
-6 -6
3n = 60
n = 20