SOLUTION: A car travels 180mi, a second car, traveling 15mi/h faster than the first car , makes the trip in 1 hr less time. Find the speed of each car.

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Question 169541: A car travels 180mi, a second car, traveling 15mi/h faster than the first car , makes the trip in 1 hr less time. Find the speed of each car.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
distance = rate multiplied by time. let r and t be rate and time of 1st car
and r+15 and t-1 be rate and time of 2nd car.
:
180=rt----------->t=180/r....eq 1
180=(r+15)(t-1)...eq 2
:
take t's value from eq 1 and substitute it into eq 2
:
180=%28r%2B15%29%28%28180%2Fr%29-1%29
:
180=%28r%2B15%29%28%28180-r%29%2Fr%29....multiply by r
180r=%28r%2B15%29%28180-r%29....distribute right side
:
180r=180r-r%5E2%2B2700-15r
:
r%5E2%2B15r-2700=0 use quadratic formula
highlight%28r=45%29 highlight%28r=-60%29 throw out negative value
:
highlight%28r=45%29 rate of 1st car
highlight%28r%2B15=60%29 rate of 2nd car:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 1r%5E2%2B15r%2B-2700+=+0) has the following solutons:

r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2815%29%5E2-4%2A1%2A-2700=11025.

Discriminant d=11025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+11025+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%2815%29%2Bsqrt%28+11025+%29%29%2F2%5C1+=+45
r%5B2%5D+=+%28-%2815%29-sqrt%28+11025+%29%29%2F2%5C1+=+-60

Quadratic expression 1r%5E2%2B15r%2B-2700 can be factored:
1r%5E2%2B15r%2B-2700+=+1%28r-45%29%2A%28r--60%29
Again, the answer is: 45, -60. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B15%2Ax%2B-2700+%29