SOLUTION: system of linear equations A cyclist traveled a certain distance at her usual speed. If her speed had been 2 mi/hr faster, she would have traveled the distance in 1 hr less time

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Question 924748: system of linear equations
A cyclist traveled a certain distance at her usual speed. If her speed had been 2 mi/hr faster, she would have traveled the distance in 1 hr less time. If her speed had been 2 mi/hr slower, she would have taken 2 hr longer. Find the distance traveled and her usual speed.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r, usual speed


____________________speed__________time__________distance
Usual________________r_____________t_____________d
Faster______________r+2___________t-1____________d
Slower______________r-2___________t+2____________d


EQUATIONS
system%28rt=d%2C%28r%2B2%29%28t-1%29=d%2C%28r-2%29%28t%2B2%29=d%29
-
system%28rt=d%2Crt%2B2t-r-2=d%2Crt-2t%2B2r-4=d%29
-
system%28rt=d%2Cd%2B2t-r-2=d%2Cd-2t%2B2r-4=d%29
-
system%28rt=d%2C2t-r-2=0%2C-2t%2B2r-4=0%29

Use the second and third equations of the simplified system and the Elimination Method to get values for r and for t. You can then use them in any of the equations to find value for d.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
system of linear equations
A cyclist traveled a certain distance at her usual speed. If her speed had been 2 mi/hr faster, she would have traveled the distance in 1 hr less time. If her speed had been 2 mi/hr slower, she would have taken 2 hr longer. Find the distance traveled and her usual speed.


Normal speed:  highlight_green%286%29 mph

Distance:     highlight_green%2824%29 miles

You can do the check!! 

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