1.5 Use Problem Solving Strategies and Models
Example 1
Use
a formula
A bus travels at an average rate of 55 miles per
hour. The distance between
Solution
Use the distance formula for distance traveled
as a verbal model.
|
Distance
(miles) |
= |
Rate
(mi/h) |
· |
Time
(hours) |
_2130_ = _55_ • t
An equation for this situation is _2130_
= _55_ t. Solve for t.
_2130_ = _55_ t Write equation.
_38.7_
»
t Divide each
side by _55_.
The amount of time it would take to travel from
55
CHECK You can use
unit analysis to check your answer.
miles
_2130_
miles » ·
_38.7_ hours
hours
Example 2
Look
for a pattern
The table shows the height h of a jet
airplane t minutes after beginning its descent. Find the height of the
airplane after 9 minutes.
|
Time
(min), t |
0 |
1 |
2 |
3 |
4 |
|
|
Height
(ft), h |
35,000 |
32,000 |
29,000 |
26,000 |
23,000 |
|
Solution
The height decreases
by 3000 feet per minute.
35,000 32,000 29,000 26,000 23,000
-3000 -3000 -3000 -3000
You can use this pattern to write a verbal model
for the height.
S
|
Height
(feet) |
= |
Initial
height (feet) |
- |
Rate
of descent (feet/min) |
· |
Time
(min) |
h = _35,000_ - _3000_ • t
An equation for the height is h = _35,000_
-
_3000_ t.
So, the height after 9 minutes is h
= _35,000_ - _3000_
(_9_) = _8000_ feet.
Example 3
Draw
a diagram
You want to paint five 1 foot wide stripes on
the wall. There should be an equal amount of space between the ends of the wall
and the stripes and between each pair of stripes. The wall is 14 feet long. How
far apart should the stripes be?
Begin by drawing and
labeling a diagram, as shown at the right.
From the diagram, you can write and solve an
equation to find x.
|
x + 1 + x + 1 + x
+ 1 + x + 1 + x + 1 + x = 14 |
Write equation. |
|
_6
x_ + _5_ = 14 |
Combine like terms. |
|
_6_x
= _9_ |
Subtract _5_ from each side. |
|
x
= _1.5_ |
Divide each side by _6_. |
The stripes should be painted _1.5_ feet
apart.