SOLUTION: On a pleasure trip, Bells drive their car a distance of 150 km at a rate of 30 kph faster than the rate they drive their boat a distance of 50 km. If the total time of the trip is

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Question 884705: On a pleasure trip, Bells drive their car a distance of 150 km at a rate of 30 kph faster than the rate they drive their boat a distance of 50 km. If the total time of the trip is 5 ½ hours, how fast do they drive each vehicle? (How to solve this using 1 Variable only? PLEASE? )
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
150km%2F%28b+%2B+30kph%29+%2B+50km%2Fb+=+5.5hr |Multiplying thru by b(b+30) so as all denominators = 1
150b + 50(b+30) = 5.5b(b + 30)
5.5b^2 -35b -1500 = 0 (Tossing out the negative solution for unit measure)
b = 20kph and car is 50kph
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5.5x%5E2%2B-35x%2B-1500+=+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=%28-35%29%5E2-4%2A5.5%2A-1500=34225.

Discriminant d=34225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--35%2B-sqrt%28+34225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+34225+%29%29%2F2%5C5.5+=+20
x%5B2%5D+=+%28-%28-35%29-sqrt%28+34225+%29%29%2F2%5C5.5+=+-13.6363636363636

Quadratic expression 5.5x%5E2%2B-35x%2B-1500 can be factored:
5.5x%5E2%2B-35x%2B-1500+=+5.5%28x-20%29%2A%28x--13.6363636363636%29
Again, the answer is: 20, -13.6363636363636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5.5%2Ax%5E2%2B-35%2Ax%2B-1500+%29