SOLUTION: Rachel is driving to an appointment. at her current speed she will be 11 minutes late and her destination is still 68 miles away. she increses her speed by 6 miles per hour and arr

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Question 904999: Rachel is driving to an appointment. at her current speed she will be 11 minutes late and her destination is still 68 miles away. she increses her speed by 6 miles per hour and arrives on time. what was her original speed?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
r original speed
68/r -68/(r+6) = 11/60 hr |Multiplying thru by r(r+6) so as all denominators = 1
68*6 = (11/60)r(r+6)
11r^2 +66r - 60*68*6 = 0 (Tossing out the negative solution for unit measure)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 11x%5E2%2B66x%2B-24480+=+0) has the following solutons:

x%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=%2866%29%5E2-4%2A11%2A-24480=1081476.

Discriminant d=1081476 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-66%2B-sqrt%28+1081476+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2866%29%2Bsqrt%28+1081476+%29%29%2F2%5C11+=+44.2700174048471
x%5B2%5D+=+%28-%2866%29-sqrt%28+1081476+%29%29%2F2%5C11+=+-50.2700174048471

Quadratic expression 11x%5E2%2B66x%2B-24480 can be factored:
11x%5E2%2B66x%2B-24480+=+11%28x-44.2700174048471%29%2A%28x--50.2700174048471%29
Again, the answer is: 44.2700174048471, -50.2700174048471. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+11%2Ax%5E2%2B66%2Ax%2B-24480+%29