Name___________________________________ Date____________
Period________
SOLVING MULTII-STEP WORD PROBLEMS WORKSHEET
1. Moe Tell starts washing dishes at the Greasy Spoon Café. Fifteen minutes later Fran
Tick joins Moe, and both wash until all the dishes are done. Moe washes 9 dishes per
minute and Fran washes 16 dishes per minute.
Define the variable m as the number of
Write an expression for the number of minutes
minutes Moe has been washing dishes.
Fran has been washing dishes (this should be in
terms of the variable you defined to the left.)
Write an expression for the number of
dishes Moe has washed after m minutes.
Use the two above expressions to
write an expression for the total
number of dishes that have been
washed.
Write an expression for the number of dishes Fran
has washed.
Use the expression for total dishes washed to write an
equation stating that 760 dishes have been washed.
Now solve that equation to find out how long that took. Don’t
forget to label your answer.
Now use the expressions
for the number of dishes
to write a new equation
stating that they have
washed the same
number of dishes.
Now solve that equation to find out
how long that took. Don’t forget to
label your answer.
How many of those did
Moe wash? How many
did Fran wash?
How many did each wash?
2. Phil T. Rich has $100 and spends $3 per day. Earnest Worker has only $20 but is
adding to it at a rate of $5 per day.
Let d be the number of days that have
Write an expression for the total amount of
passed. Define d.
money Phil has after d days.
Write an expression for the total amount of
money Earnest has after d days.
Now use the expressions for the
money each person has to write an
equation stating that they have the
same amount of money.
How much money will they each have?
Who has more money and how much more after 2
weeks?
Now solve that equation to find out how long that took.
Don’t forget to label your answer.
3. Nick O’Time, the plumber, charges $30 per hour. His brother Ivan, the plumber’s
helper, charges $20 per hour. Nick starts working on a job. Four hours later Ivan joins
him and both work until the job is finished.
Let t be the number of hours Nick has worked. Write an expression for the number hours Ivan
Define t.
has worked on the job (this should be in terms
of the variable you defined to the left.)
Write an expression for the number of
dollars Nick has earned.
Use the two above expressions to
write an expression for the total
amount of money they have earned
together.
Write an expression for the number of dollars
Ivan has earned.
Use the expression for total money to find out how
much money to write an equation stating they have
earned $470 together.
Now solve that equation to find out how long that took. Don’t
forget to label your answer.
How much money did
Nick make? How much
did Ivan make?
4. Suppose that you turn the hot water on and it flows at a rate of 8.7 liters per minute
into the bath tub. Two minutes later you also turn the cold water on which flows at a rate
of 13.2 liters.
Write an expression for the number of minutes
Let x be the number of minutes that have
the hot water has been running.
passed since you turned the cold water on.
Define x.
Write an expression for the number of liters Write an expression for the number of liters the
the cold faucet has delivered.
hot faucet has delivered.
Use the two above expressions to
write an equation stating that the hot
and cold faucets have delivered the
same number of liters.
Now solve that equation to find out how long that took.
Don’t forget to label your answer.
The tub holds 100 liters. Will it have overflowed by the time the hot and cold faucets have
delivered the same amounts? Justify your answer.
5. A cougar spots a fawn 132 meters away. The cougar starts toward the fawn at a speed of 18
meters per second. At the same instant the fawn starts running away at 11 meters per second.
Draw a rough sketch of the situation:
Let x be the number of seconds they have been running. Define x.
Write an expression for the distance the
cougar is from his starting point.
Use the two above expressions to
write an expression for the distance
the cougar is from the fawn after x
seconds.
Use the expression for
the distance the cougar
is from the fawn to write
an equation stating that
the distance between the
cougar and the fawn
equals 60 meters.
Write an expression for the distance the fawn is
from the cougar’s starting point.
Use the expression for the distance the cougar is from
the fawn to find how far the cougar is from the fawn
after 8 seconds. Don’t forget to label your answer.
Now solve that equation to find out how long that took. Don’t
forget to label your answer.
The cougar has enough energy to run for a total of 17 seconds. Will it catch the fawn before it runs out
of energy? Justify your answer.