Math Word Problem Example “Tony the Tigers Bathtub Dilemma”
Tony the Tiger got very dirty
playing baseball he is trying to fill a bathtub to take a bath. He turns the
hot water on and it is pumping 8 gallons per minute. He then turns the cold
water on two minutes later and it is pumping 12 gallons per minute. By making X
equal the number of minutes that have passed since you started the water find
out how many minutes will have passed until there is an equal amount of cold
and hot water in the tub.
UNDERSTANDING THE PROBLEM A) What am I trying to do?
-Solve for x
when the equations are equal to each other.
8x = T
12(x-2)
= T
8x=12(x-2)
B) Where am I?
-
Two equations that are equal to each
other.
8x
= 12(x-2)
DEVISE A PLAN C) Can I relate this to
any other
problem
that you have done?
-I might have
done something like
this.
4x = 16 or x + 2
= 6
D) What do I need to do now?
-Isolate x onto one side of the equation.
CARRY OUT THE PLAN E) 8x = 12x-24
-12x -12x
-4x = -24
-4 -4
x = 6
CHECK THE
STEPS F) What can I do to see if this makes
sense?
-Plug
6 back into the equation as x
and
see if the two equations are
equal
to each other.
8(6)=12(6-2)
48
= 48
- This means that it takes 6 minutes for the bathtub to have an equal amount of hot water and cold water
Example #2:
The
temperature in Phoenix, Arizona at 4:00pm is 100 degrees F . Every hour the
temperature decreases by 4 degrees F. The temperature in Anchorage, Alaska at
9:00am is 30 degrees F. Every hour the temperature increases by 6 degrees F.
Non-linear steps to Problem Solving:
1.
Understand the problem - a. What are you trying to do here?
- solve for x so that the
temperatures are equal
2.
Devise possible plans - a. Is there an idea of what you’re going to do?
- create 2 equations
b. Do you already know what x is?
- x is the number of hours
c. What is the plan?
- create two equations, set them
equal to eachother, and solve for
x.
3.
Carry out one plan - a.
What can you do first?
- create the 2 equations: 100 - 4x = T , 30 + 6x = T
- set the equations equal to one
another
100
– 4x = 30 + 6x
b.
What do you do next?
- isolate x: 70 = 10x ,
7 = x
4.
Check the steps - a.
What does this mean?
- it takes 7 hours for the two
temperatures to become equal
b. Does this make sense?
- yes, if it takes seven hours for
the two temperatures to become equal , then the time in Anchorage, Alaska would
be 4:00pm and the time in Phoenix, Arizona would be 11:00pm. These temperatures
make sense.
Now it is your turn:
Bill has 2
pieces of rope. One piece is 7 feet 6 inches long and the other is 12 feet 3
inches long. Bill needs two pieces of rope that are both 6 feet 3 inches long
for a knot tying contest. The only problem with cutting the rope is Bill only
has a 3 inch ruler. How many times will bill have to cut each rope?
Math Writing Word Problem
Assignment “ Captain Crunch’s Sinking Boat Problem”
Pirates attacked Captain Crunches boat full of cereal trying to get the treasure. They succeeded in putting a hole on the side of the boat. Cereal was pouring out and water was getting in. Luckily for Captain Crunch and his cereal there are pumps on the boat that can pump a certain amount of water out so they wont sink. The water is coming in at a rate of 5 gallons per minute and it can be pumped out at a rate of 7 gallons per minute, but by the time the pump is turned on there is already 100 gallons of water in the boat. Make X the number of minutes and find out when there won’t be any water in the boat and Captain Crunch will be able to patch the hole.