Using Rational Equations Motion Problem The distance formula d rt or r dt or t dr You may want to find the following table helpful in solving motion problem Distance ID: 645733
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Slide1
Sections 6.7
Applications
Using Rational EquationsSlide2
Motion Problem
The distance formula:
d =
rt or r = d/t or t = d/r You may want to find the following table helpful in solving motion problem.
Distance
Rate/speed
Time
Quantity 1/Case
1
Quantity
2/ Case 2Slide3
Example 1
The top speed of car A is 33 mph less than the top speed of car B. At their top speeds, car B can travel 6 miles in the same time that car A can travel 5 miles. Find the top speed of each car.
Let x be the top speed of car A
Then (x + 33) is the top speed of car BSlide4
Solution
The top speed of car A is
The top speed of car B is
Distance
(miles)Rate/speed (mph)Time(hours)
Car A
x
Car B
x + 33 Slide5
Example 2
A fisherman travels 9 miles downstream with the current in the same time that he travels 3 miles upstream against the current. If the speed of the current is 6 mph, what is the speed at which the fisherman travels in still water
?
Let x be the speed at which the fisherman travels in still water.
6mph
Distance
(miles)
Rate/speed
(mph)
Time
(hours)
Down
stream
x + 6
Upstream
x – 6
Slide6
Share-Work Problems
Rate of work
:
If a job can be completed in
t units of time, then the rate of work is 1/tSimilar to the distance formula, we have the following
Work completed = rate
x
time
or
W =
rt
Slide7
Example 3
Joe can paint a house in 3 hours
.
Sam can paint the same house in 5 hours.
How long does it take them to paint together?Answer:
http://www.youtube.com/watch?v=VnOlvFqmWEY
Slide8
Example 4
The CUT-IT-OUT lawn mowing company consists of two people: Tina and Bill. If
Bill cuts
a lawn by
himself, he can do it in 4 hrs. If Tina cuts the same lawn herself, it takes her an hour longer than Bill. How long would it take if they worked together?Slide9
Ratios
The
ratio
of a to b is
or a to b or a:bA Proportion is a statement that two ratios are equal. In other words, a proportion has the formSlide10
Examples
Solve the following proportionsSlide11
Example
Billie earns $412 for a 40-hour week. If she missed 10 hours of work last week, how much did she get paid?Slide12
Similar TrianglesSlide13
Example
A tree casts a shadow 18 ft long at the same time as a woman 5 feet tall casts a shadow 1.5 feet long. Find the height of the tree.