SOLUTION: I have three problems I could use help solving. All of them need to include a table used to derive an equation. They can be solved by the quadratic equation or factoring. Here are

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Question 856256: I have three problems I could use help solving. All of them need to include a table used to derive an equation. They can be solved by the quadratic equation or factoring. Here are the problems.
The diagonal of a square is 30 feet. Find the length of a side of the square (give exact answer and an approximation to the nearest tenth of a foot).
By splitting up the problems, Michael and Janessa can do a homework assignment in 30 minutes. Janessa alone can do the same assignment in 25 minutes less time than Michael. Find the time it takes each of them to do the assignment alone.
Vivek was riding his bike to school. He lives 3 miles away from Friedell. After riding a mile, he ran over a broken bottle and popped a tire. He had to walk his bike the rest of the way. Walking was three miles per hour slower than riding his bike. The total trip to school took him 1 hour. Find his speed riding his bike and his speed walking.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Vivek bike problem seems to be the more complicated exercise you have.

Only can guess that Friedell is the school for the destination.
Let r = biking speed

______________speed__________time___________distance
Biking________r______________(___)______________1
Walking______r-3_____________(___)______________2=3-1
Total_________________________1_________________3

Fill in the time expression using RT=D as T=D/R.

______________speed__________time___________distance
Biking________r______________1/r______________1
Walking______r-3_____________(2/(r-3))________2=3-1
Total_________________________1_______________3

Time sum equation uses only one variable, r.
highlight%281%2Fr%2B2%2F%28r-3%29=1%29 LCD is r%28r-3%29;
Multiply members by r%28r-3%29;
r-3%2B2r=r%5E2-3r
cross%28r%5E2-3r-r%2B3=0%29------MISTAKE HERE.
r%5E2-3r-2r%2B3=0-------CORRECTED.
r%5E2-5r%2B3=0 NOT FACTORABLE.
discriminant=25-4*3=25-12=13
r=%285%2B-+sqrt%2813%29%29%2F2-----but not reasonable to have both values.
r=%285-sqrt%2813%29%29%2F2 or highlight%28r=%285%2Bsqrt%2813%29%2F2%29%29
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The subtraction form will make no sense, because then the walking speed would become negative.
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FINISHED ANSWER: The plus form must be chosen. That one is near to 4.3 mph; Riding speed is 4.3 mph and walking speed is 1.3 mph.