Name
CHAPTER
1
Date
Extended Problem Solving
Use after Lesson 1.5
Problem solving strategies such as make a table, guess and check, and work backward
can be used to solve rate and other multi-step problems.
EXAMPLE 1
Make a table
Two pipes are used to drain water from a pool. One pipe can drain all the water in
12 hours. The other pipe can drain all the water in 20 hours. How many hours will it
take both pipes to drain the water if used together?
Solution:
Let h represent the hours it takes both pipes to drain the water from the pool. Make
a table to find the fractional amount of water drained by each pipe in h hours.
Pipe
Fraction of Water
Drained in 1 Hour
Hours Both
Pipes Drain
Fraction of Water
Drained in h Hours
1
}
1
12
h
}
2
}
1
20
h
}
h
h
12
h
20
h
The equation }
1}
5 1 can be used to find the time it takes both pipes together to
12
20
drain 1 pool.
h
12
h
20
Write the equation.
5h 1 3h 5 60
Multiply each side by 60, the LCM of 12 and 20.
8h 5 60
Simplify.
h 5 7.5
Divide each side by 8.
It takes 7.5 hours for both pipes to drain the pool together. N
EXAMPLE 2
Guess and check
Two trains leave a station at the same time, traveling in opposite directions. The faster
train moves at a rate of 60 miles per hour. The slower train moves at a rate of 40 miles
per hour. After how many hours will the trains be 150 miles apart?
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}1}51
Solution:
Guess a time and find the distance the trains are apart at that time. Guess until you find
the time when the trains are 150 miles apart. Use a table to organize each guess.
Guess
Faster Train
Distance
Slower Train
Distance
Total Distance
Apart
Result
1 hour
60 miles
40 miles
100 miles
too low
2 hours
120 miles
80 miles
200 miles
too high
1.5 hours
90 miles
60 miles
150 miles
correct
The trains are 150 miles apart after 1.5 hours. N
Algebra 2
Best Practices Toolkit
343
Name
CHAPTER
1
Date
Extended Problem Solving
continued
Use after Lesson 1.5
EXAMPLE 3
Work backward
Peter is making a casserole for dinner. He wants the dinner to be ready at 7:30. The
casserole takes 20 minutes to prepare, 45 minutes to bake, and 10 minutes to cool.
What time should Peter start making the casserole?
Solution:
Work backward from 7:30 to find the time to start making the casserole. Start by
subtracting the cooling time.
7:30 2 10 minutes 5 7:20
Subtract the cooling time.
7:20 2 45 minutes 5 6:35
Subtract the baking time.
6:35 2 20 minutes 5 6:15
Subtract the preparation time.
Peter should start making the casserole at 6:15 to have it ready at 7:30. N
Practice
1. During one week, the value of a stock dropped 16 cents Monday, dropped
12 cents Tuesday, rose 8 cents Wednesday, rose 13 cents Thursday and dropped
6 cents Friday. The value of the stock at the end of Friday was $49.26. What was
the value of the stock at the start of the week?
2. Joe enters 300 pieces of data into the computer each hour. Troy enters 400 pieces
of data each hour. Together they entered 3500 pieces of data. How many hours
did this take?
$6 more than the second day but $16 less than the third day. What amount did
Stacie earn the first day of babysitting?
4. Two trucks travel a combined distance of 600 miles in 5 hours. The average rate
of speed of one truck is 20 miles per hour faster than the other truck. Find the
average speed of both trucks.
5. Jordan’s phone company charges a basic monthly fee of $28.80 and $0.15
a minute for long distance calls. Last month, Jordan’s phone bill was $52.29
including a 5% tax. How many minutes of long distance calls were on Jordan’s
phone bill?
6. A designer can make the scenery for a school play in 6 hours. Her assistant can
make the scenery in 10 hours. How many hours will it take the designer and her
assistant to make the scenery if they work together?
1
7. While on a treadmill, Marlena walked 2 miles an hour for } of the time and
3
2
1
4 miles an hour for }3 of the time. She walked a total of 2}2 miles. What amount
of time, in hours, did Marlena walk on the treadmill?
8. Theresa travels 48 miles by car in the same time it takes her to travel 12 miles
on her bike. Her average rate of speed by car is 24 miles per hour faster than her
average rate of speed by bike. What is the average rate of speed for both the car
and the bike?
344
Algebra 2
Best Practices Toolkit
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Pre2AP Copymasters
3. Stacie earned $82 babysitting over a three day period. On the first day, she earned