SOLUTION: A 150 mile trip is driven at R miles per hour. The same trip would take 2 hours less if you increase the speed by 20 mph. What is R? I have tried R=150/t R=150/t-2 (150/t+2=150/

Question 28932: A 150 mile trip is driven at R miles per hour. The same trip would take 2 hours less if you increase the speed by 20 mph. What is R? I have tried R=150/t
R=150/t-2 (150/t+2=150/t-2).t(t-1)= 150t-150t+2t2-2t= t2-t-150=0 = (t+2)(t+75)and that is as far as I get because I know that that is not right.
Thank you for your help. These always put me in a tail spin. Cheryl Vogel
Found 2 solutions by Paul, stanbon:
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
let the normal speed be
If increased by 20 the speed will be x+20
Subtract the increase speed by the normal speed respect to the distance = time.

Equation:

a=1, b=20, c=-1500

Simplfy that and you get 2 solutions:

x=-50 and x=30

Remove the negative

Hence, the normal speed (R) is 30mph.
Paul.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
original data: 150=Rt. So, t=150/R
Modified time and rate result in the following:
150=(R+20)(t-2)
Substitue for "t" to get:
150=(R+20)[(150/R)-2]
150=150-2R+3000/R-40
0=-2R^2+3000-40R
0=2R^2+40R-3000
0=R^2+20R-1500

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=6400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 30, -50. Here's your graph:

Hope this helps.
Cheers,
Stan H.

RELATED QUESTIONS
Average Speed, Each week you must make a 180-mile trip to pick up supplies for your... (answered by ewatrrr)
If the speed were increased by 10mph, a 420-mile trip would take 1 hour less time. How... (answered by ankor@dixie-net.com)
Please check my work, thank you. Practical Application of Quadratic Equations 1. (answered by yuendatlo)
A women drives her snowmoble 150 miles at the rate of r mph. She could have gone the same (answered by stanbon)
A car travels for 100 miles at a uniform speed. If the speed is increased by 5 miles per... (answered by josmiceli)
A car travels for 100 miles at a uniform speed. If the speed is increased by 5 miles per... (answered by TimothyLamb)
A car travels for 100 miles at a uniform speed. If speed is increased by 5 miles per... (answered by ikleyn)
a cyclist traveled the first 12 miles of a 30 mile trip at an average speed of 15 miles... (answered by ankor@dixie-net.com)
If the speed were increased by 10mph, a 420 mile trip wud take and hour less. how long... (answered by Nate)