SOLUTION: Sandy made a trip to a city 200 miles away and then returned home. Her average speed on the return trip was 10 mph less than her average speed going. If her total travel time was 9

Question 1034960: Sandy made a trip to a city 200 miles away and then returned home. Her average speed on the return trip was 10 mph less than her average speed going. If her total travel time was 9 hours, what was her average rate in each direction?
Found 2 solutions by Alan3354, addingup:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Sandy made a trip to a city 200 miles away and then returned home. Her average speed on the return trip was 10 mph less than her average speed going. If her total travel time was 9 hours, what was her average rate in each direction?
-------------
r = speed going
---
d = r*t
t = d/r
200/r + 200/(r-10) = 9
200(r-10) + 200r = 9r(r-10)
400r - 2000 = 9r^2 - 90r
9r^2 - 490r + 1910 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=171340 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 50.218464534692, 4.22597990975241. Here's your graph:

==================
r = 50.22 going, 40.22 returning
----
Ignore the 4... solution, subtracting 10 would give a negative speed.
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
200 out
200 back
9 hrs total
d= st
d/s = t

Multiply times -1

or
or ;
So, on the way out her speed was 50mph and on the return 50-10=40
``````````````````````````````````````````````````
Check:
50+40 = 90; 90/2 = 45; 45*9 = 405 it should be 400, the 5 is the result of rounding numbers. So the answer is correct.
RELATED QUESTIONS
Paul drove to the city, 200 miles away, and returned home at the speed which was 10 mph... (answered by mananth)
a man drove at a constant speed from his city 180 miles away. On the return trip, he... (answered by mananth,lwsshak3)
A trucker drove 180 miles to make a delivery and returned home on the same route. Because (answered by mananth)
Kari took her new motorcycle for a drive to a town 300 miles away and then back home.... (answered by josmiceli)
Jennifer drove 300 miles to see her friend. On the return trip, she drove 10 mph faster,... (answered by josgarithmetic,ikleyn,greenestamps,MathTherapy)
A trucker drove 72 miles to make a delivery and returned home on the same route. Because... (answered by josgarithmetic)
A trucker drove 140 miles to make a delivery and returned home on the same route. Because (answered by greenestamps)
Wilma drove at an average speed of 35 mph from her home in City A to visit her sister in... (answered by ankor@dixie-net.com)
Jose drove 15 miles to pick up his sister and then returned home. On the return trip, he (answered by ankor@dixie-net.com)