SOLUTION: It's 90 miles from Ayville to Beeville. It's another 195 miles from Beeville to Charleston. Chad drives 20 miles per hour faster from Beeville to Charleston than from Ayville to Be

Algebra.Com
Question 1175351: It's 90 miles from Ayville to Beeville. It's another 195 miles from Beeville to Charleston. Chad drives 20 miles per hour faster from Beeville to Charleston than from Ayville to Beeville. If his combined travel time is 5 hours, what are his average speeds?
Speed from Ayville to Beeville:?
Speed from Beeville to Charleston:?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39614)   (Show Source): You can put this solution on YOUR website!
            SPEED       TIME           DIST.
AtoB        r           90/r            90
BtoC        r+20        195/(r+20)      195
TOTAL                    5

Continue with equation , and solve it for r,...
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.

The time equation is


     +  = 5 hours.


The solution you can guess mentally:  r = 45 km/h from A to B.


Then the average speed from B to C is 45+20 = 65 km/h.



By the way, notice that the left side of the equation is the function of "r", 

monotonically decreasing with variable "r" in positive domain.


So, if you guess one solution, you can be sure that this solution is UNIQUE and there is NO other solution.


So, such "guessing", accompanied with noticing about monotonicy is logically absolutely strict way to solve the problem.



Alternatively, you may reduce the problem to quadratic equation and solve it.



In any case, from my post you just know the answer.




RELATED QUESTIONS

It is 185 miles to Fort Worth. If Vang drives 2 hours at 65 miles per hour, how far... (answered by MathLover1)
Sarah wants to arrive at her friend's wedding at 3:00 PM. The distance from Sarah's house (answered by math_tutor2020)
Travis lives 195 miles from Dallas. On a normal trip, it takes 180 minutes to drive from... (answered by Alan3354)
a car travels at an average of 52 miles per hour. how long does it take to travel 195... (answered by jim_thompson5910)
The time T  it takes to drive from Houston to Denver is inversely proportional to... (answered by rfer)
It takes Chrissy 35 mins to drive to work when she drives 50 miles per hour how long will (answered by josmiceli)
Bert drives his car from home 40 miles per hour going to work and 50 miles per hour... (answered by josgarithmetic)
wilson is 20 miles from your house and you can drive 20 miles per hour. How long would it (answered by Fombitz,Razzak Ahmed)
How long does it take to travel from point A to point B, a distance of 25 miles... (answered by stanbon)