Algebra I from a thick red book written by Dolciani. Since then we have
had many modifications of that book as we have started to emphasize
graphing over story problems. However, we still have to be able to solve
those problems you loved so much.
Example: One plane leaves Chicago, fling east at 400
M.P.H.. A second plane leaves one hour later fling
west at 500 M.P.H.. When will they be 1800 miles
apart?
We will solve this problem in a moment, but we should first talk about
all of these types of problems. It is all about the DISTANCE. In all of
these problems we will know one of 3 things.
- The sum of the distances
- The difference of the distances
- The distances are equal
Now lets look at our problem above.
FIRST: When will they be 1800 miles apart?
SECOND: Draw a PICTURE
← ⎮→
500 M.P.H. 400 M.P.H.
.__________________________________________.
1800 Miles
DISTANCE RATE TIME
d₁ 400 T
d₂ 500 T–1
THIRD: Make an equation.
400T + 500(T–1) = 1800
400T + 500T – 500 = 1800
900T – 500 = 1800
900T = 2300
T = 23/9 Hours
T = 2 and 5/9 Hours
T = 2 hours 33 minutes and 20 seconds
The planes are 1800 miles apart in 2 hours 33 minutes
and 20 seconds.
I know it seems easy when someone else does it, but if we know patterns
just follow the pattern I created. After doing a few of them you using a
picture and a DIRT BOX it should be easy for you.
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