1. Solving word problems
work distance

2. Example: Using Work Formula
To solve problems involving work, use the formula,
part of work completed = rate of work time worked.
Example: If it takes 5 hours to paint a room, what part of the work is completed after 3 hours?
If one room can be painted in 5 hours then the rate of work is (rooms/hour). The time worked is 3 hours.
Therefore, part of work completed = rate of work time worked
part of work completed
Three-fifths of the work is completed after three hours.
Example: Using Work Formula

3. Let t be the time it takes them to paint the room together.
Example: If a painter can paint a room in 4 hours and her assistant can paint the room in 6 hours, how many hours will it take them to paint the room working together?
Let t be the time it takes them to paint the room together.
painter
assistant
rate of work
time worked
part of work completed t t
LCM = 12.
Multiply by 12.
Simplify.
Working together they will paint the room in 2.4 hours.
Example: Word Problem

4. Marge can clean the house in 3 hrs.
Lisa can clean it in 5 hrs.
How long will it take them to clean the house if they both work together?

5. Marge can clean the house in 3 hrs.,
Use Unit Rates
Marge can clean the house in 3 hrs.,
so she does 1/3 of the house per hour.

6. Lisa can clean the house in 5 hrs.,
Use Unit Rates
Lisa can clean the house in 5 hrs.,
so she does 1/5 of the house per hour.

7. Let T be the time in hours.1 1 T + T = 1 3 5

8. 1/3T + 1/5T = 1
15(1/3T + 1/5T) = 15(1)
5T + 3T = 15
8T = 15
T = 15/8
17/8 hrs.

9. Think of the problem in terms of hourly units…
Mr. Love can paint a room in 3 hours. Mr. Sexton can paint the same room in 6 hours. How many hours will it take them to paint the room together? + =

10. 18t ● 6 3 1 1 1 t # 6 3 9t

11. Examples: Using Motion Formulas
To solve problems involving motion, use the formulas,
distance = rate  time and time =
Examples: 1. If a car travels at 60 miles per hour for 3 hours, what distance has it traveled?
Since rate = 60 (mi/h) and time = 3 h, then
distance = rate time = = 180.
The car travels 180 miles.
2. How long does it take an airplane to travel miles flying at a speed of 250 miles per hour?
Since distance = 1200 (mi) and rate = 250 (mi/h),
time = = = 4.8.
It takes 4.8 hours for the plane make its trip.
Examples: Using Motion Formulas

12. Example
Bike riders Brent and Jane started at noon from points 60 km apart and rode toward each other, meeting at 1:30pm. Brent’s speed was 4km/h greater than Jane’s speed.
Find their speeds.

13. Chart x = r 1.5 1.5r r + 4 1.5 1.5(r + 4) BIKE RIDING RATE TIME
DISTANCE
JANE
BRENT r
1.5
1.5r
r + 4
1.5
1.5(r + 4)

14. Brent’s speed was 22km/h and Jane’s speed was 18 km/h
Equation
1.5 ( r + 4) + 1.5r = 60
r = 18 Jane’s speed
r + 4 = 22 Brent’s speed
Brent’s speed was 22km/h and Jane’s speed was 18 km/h

15. Try This
At noon a private plane left Austin for Los Angeles, 2100km away, flying at 500 km/h. One hour later a jet left Los Angeles for Austin at 700km/h. At what time did they pass each other?

16. 500t + 700(t – 1) = 2100
TRAVEL
RATE
TIME
DISTANCE
PLANE
JET

17. 500t + 700(t – 1) = 2100
500t +700t – 700 = 2100
1200t – 700 = 2100
+700 =+700
1200t = 2800
1200t/1200 =2800/1200
T=2 and 400/1200 HRS or 2 and 1/3hrs is 2hrs 20min
WHATS THE QUESTION Airplane took 2 hours and 20 min before meeting with
Jet that took t – 1 =2hr 20 min – 1 = 1hr and 20 min
Time is 12: hr and 20 min . They jet passed the plane at 2:20

18. Let r be the rate of travel (speed) in miles per hour.
Example: A traveling salesman drives from home to a client’s store 150 miles away. On the return trip he drives 10 miles per hour slower and adds one-half hour in driving time.
At what speed was the salesperson driving on the way to the client’s store?
Let r be the rate of travel (speed) in miles per hour.
Trip to client
Trip home
distance
rate
time
150 r
150
r – 10
LCM = 2r (r – 10).
300r – 300(r – 10) = r(r – 10)
Multiply by LCM.
Example continued
Example: Word Problem

19. The return trip took one-half hour longer.
Example continued
300r – 300r = r2 – 10r
0 = r2 – 10r – 3000
0 = (r – 60)(r + 50)
r = 60 or – 50
(–50 is irrelevant.)
The salesman drove from home to the client’s store at 60 miles per hour.
Check:
At 60 mph the time taken to drive the 150 miles from the salesman’s home to the clients store is = 2.5 h.
At 50 mph (ten miles per hour slower) the time taken to make the return trip of 150 miles is = 3 h.
The return trip took one-half hour longer.
Example Continued