Time (t)Problem Solving Using
Algebraic Models
Problem: A man drove 700 miles to L.A. with an average speed of 65 mi/h. what was the time it took him to get to L.A. in this time?
Formula: Distance (d) = Rate (r) Time (t)
Step One:
Find what you "know" to find the answer.
A man drove 700 miles to L.A. with an average speed of 65 mi/h. what was the time it took him to get to L.A. in this time?
Step Two:
Plug in what you "know"
700 miles = 65 mi/h t (What you want to know)
Step Three:
Do the work.
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t = 10.8 Hrs
Step Four:
Check your work.
700 = 6510.8 (It's okay to round up)
65 x 10.8 = 700
*What we learned
1) Find what you know
2) Plug it in
3) Solve
4) Check Work
Ex 1.
A lady bug decides to get up and fly from one bush to another bush. It's average speed was 5 mph, and it took the ladybug 8 seconds to arrive to the perfect leaf. What distance did it travel?
Step one:
d = 5 mph 8 sec
Step two:
d = 5 8
d = 40 miles
Step four:
40 = 5 8
*Remember, the formula works to find any of the three. So if you know two you will always be able to find the last one.
Solve These Problems
1) A man has to travel 200 miles by boat to Portland, how long will it take him if you ignore air resistance and he travels at 90 mph?
2) The same man now needs to travel back from Portland, 900 miles. He's traveling at a rate of 160 mph, the wind is also pushing him at 15 mph. How long will it take him to get to his new destination with 2 tanks full of gas?
*KEY