Rate & Work Problems
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Rate & Work Problems
Rate Problems: A rate is way of expressing how fast something occurs such as mi/hr (rate of speed) or $/hr (rate of earning).
Ex: If the car is travelling at 30 miles per hour, we say its rate of speed is 30 mi/hr. If it travels constantly at this speed for 10 hours, how far will it go?
Strategy to solve:
1) ____________________________________
2) ____________________________________
3) ____________________________________
4) ____________________________________
d rt
Write known amounts in a table
Fill in blanks of table
Write equations using
Solve
Ex 1: During a 456-mile trip to Florida, Heather drove the first two hours at an average speed of 48 mi/hr. During the remainder of the trip, her friend Boo drove for another 8 hrs. What was Boo's average speed?
456
24896
8r360
Heather
Boo
=
=
8r = 360
r = 45 mph
456
24896
8r360
Heather
Boo
=
=
Ex 2: Train A leaves the station travelling at an average speed of 40 mi/hr. Eight hours later, Train B leaves in the same direction as Train A, but is travelling at an average speed of 60 mi/hr. How long will it be before Train B catches up to Train A?
d r t
Train ATrain B
40
60
t
t – 8
d
d
=
=
60(t – 8) = 40t
60t – 480 = 40t20t – 480 = 0
20t = 480t = 24 hrs
d r t
Train ATrain B
40
60
t
t – 8
d
d
=
=
Strategy to solve:
1) ____________________________________
2) ____________________________________
3) ____________________________________
Write fractional time for each person
Add them up to total # of jobs done
1 1#
# #t t of jobs
Ex 1: With spraying equipment, Parker can paint the wood trim on a small house in 8 hours. His assistant, Andres, must paint by hand since there is only one sprayer, and he needs 12 hours to complete the same type of job. If they work together on the same house, how long should it take them to complete the job?
1
8t
1
12t 1
1 1 1
8 12t t
24
3 2 24t t
24
5 24t
24
24
5t
44
5 hrs
Ex 2: A large water pump can fill a standard size swimming pool in 4 hours, while medium size water pump will take 6 hours to fill the same pool. Working both pumps at once, how long will it take to fill 3 standard size pools?
1
4t
1
6t 3
1 1 3
4 6t t
12
3 2 36t t
12
5 36t
12
36
5t
17
5 hrs
Decide if it is a rate or work problem, then solve.
1. Andres can split a cord of wood in 4 days. His friend Travis can split a cord in 2 days. How long would it take to split a cord of wood if they work together? (FYI: a cord of wood is a stack of wood 4 feet deep by 4 feet high by 8 feet long.)
1
4t
1
2t 1
work
1 1 1
4 2t t
4
2 4t t
4
3 4t
4
4
3t
11
3 days
2. Fernanda starts off around a go-cart track and is averaging a speed of 20 ft/s. Her friend, Ashley, starts 5 seconds later and averages 25 ft/s around the track. How long will it be before Ashley catches up to Heather?
rate
d r t
FernandaAshley
20
25
t
t – 5
d
d
=
=
25(t – 5) = 20t
25t – 125 = 20t5t – 125 = 0
5t = 125t = 25 sec
d r t
FernandaAshley
20
25
t
t – 5
d
d
=
=
3. During a 840 mile flight, a small plane averages a speed of 160 mi/hr for the first 3 hours when one engine fails. For the remaining 3 hours of the flight, its speed was reduced to what average speed.
rate
d r t
1st
2nd
160
r
3
3
480
360
=
=840
3r = 360
r = 120mph
d r t
1st 2nd
160
r
3
3
480
360
=
=840
4. Ryan and Spencer own an oak wall-unit business. Ryan can stain their large wall-unit in 3 hours and Spencer takes 4 hours. How long would it take them to stain 2 wall units if they work together?
1
3t
1
4t 2
work
1 1 2
3 4t t
12
4 3 24t t
12
7 24t
12
24
7t
33
7 hrs
HW #1
1. Andy's average speed driving on a 4 hour trip was 45 mi/hr. During the first 3 hours he drove 40 mi/hr. What was his average speed for the last hour of the trip?
distance = rate time
4
340120
1r60
1st
2nd
180
45 =
=
=
r = 60 mph
distance = rate time
4
340120
1r60
1st
2nd
180
45 =
=
=
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