Hello Class
Here are the steps and the solutions for the problems in section 6.8.
(4) Raking. Zoe can rake her yard in 4 hours. Steffi does the same job in 3 hours. How long would it take the two of them, working together,
to rake the yard?
a- Zoe - 4 hours and one hour for Zoe equals
b- Steffi - 3 hours and one hour for Steffi equals
of the job.
of the job.
is the equation that we use to find the time that it would take Zoe and Steffi to finish the job together.
The LCD for 4 and 3 is 12.
hours for Zoe and Steffi working together
(6) Plumbing. By checking work records, a plumber finds that Raul can plumb a house in 48 hours. Mina can do the same job in 36 hours.
How long would it take if they worked together?
a-Raul - 48 hours and one hour for Raul equals
b-Mina - 36 hours and one hour for Mina equals
of the job.
of the job.
The LCD of 48 and 36 is
144
(1)
7 t = 144
hours for Raul and Mina working together.
(10) Office Copiers. The HP Officejet 7410 All-In-One printer, fax, scanner, and copier, and copier can copy in color a staff training manual
in 9 minutes. The HP Officejet 4215 All-In-One can copy the same report in 15 minutes. How long would it take the two copiers, working
together, to make one copy of the manual?
a- 7410- 9 minutes which equals
b- 4215- 15 minutes which equals
reduces to
reduces to
Another way of looking at this equation would be
If you have any questions about how the transformation occurs please ask. I will be more than happy to demonstrate the
process in class.
Working this problem will be easier to solve by removing the 3 in the denominator by multiplying through by 3. This gives us
this is a fraction of an hour. It will be easier to understand if we convert it to minutes.
the
This reduces down to
cancels out and leaves
and this can be change to a mixed number of 5
minutes that it took the two copiers to work
together. Both answers are correct, on the test your answer selection may be in minutes or hours. You need to be able to convert from hours to
minutes and vice versa.
Class, remember the five step process for working application problems? On page 127 of the text book, Bittinger lists the steps and explains
them. In problem 12, I used Bittinger's 5 step process to solve the problem. Not all of the are shown. One step that is particularly useful is
using a table to categorize the information that is being collected.
(12) Car Speed. A passenger car travels 30 km/hr faster than a delivery truck. While the car goes 400 km, the truck goes 250 km. Find their
speeds.
Vehicles
distance
speed
time
Car
Truck
The car and truck both have the same time This means that we can use the same time to form equations for the car and the truck.
The formula for the car is
this formula has the model
for the car and
this formula is the same model as above. Since the time is the same for the car and the truck
400
=
250
,
,
,
,
,
The truck speed is 50 miles per hour
The car speed is 50 + 30, 80 miles per hour.
(14) Train Speed. The speed of a freight train is 15 mph slower than the speed of a passenger train. The freight train travels 390 miles in the
same time that it takes the passenger train to travel 480 miles. Find the speed of each train.
Trains
distance
speed
time
Freight
Passenger
for the freight train
for the passenger train
solve for x
The passenger train speed is 80 mph
The freight train speed is 80 minus 15 miles per hour, 65 mph
I am using Maple 13, in problem 14, I allowed the program to work the problem. Problems 12 and 14 follow the same steps in coming to a
conclusion. If you had trouble in working 12 or 14 let me know.
(16) Car Speed. After driving 126 miles, Syd found that the drive would have taken 1 hour less time by increasing the speed by 8 mph. What
was the actual speed?
Drives
distance
rate
time
drive 1
126
x
t
drive i
126
x+8
t-1
this is the formula for the first drive
,
this is the second formula for the imaginary drive
solve for x
This problem evolves into a quadratic equation that provides two answers to choose
from. In real world problems choose the positive answer. In this case, 28 miles per hour is the answer we are looking for.
The actual speed is 28 mph.
(18) Driving Speed. Kaylee's Lexus travels 30 mph faster than Gavin's Harley. In the same time that Gavin travels 75 miles, Kaylee travels
120 miles. Find their speeds.
Drives
distance
Kaylee
Gavin
Kaylee's formula
rate
time
Gavin's formula
solve for x
Kaylee's speed is 50 + 30, 80 mph
Gavin's speed is 50 mph