SOLUTION: Steve Forrester drove 25 miles at a constant speed,and then he increased his speed by 15 miles per hour for the next 65 miles.If the time required to travel 90 miles was 1.5 hours,

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Question 1132341: Steve Forrester drove 25 miles at a constant speed,and then he increased his speed by 15 miles per hour for the next 65 miles.If the time required to travel 90 miles was 1.5 hours,find the speed he drove during the first 25 miles.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
                   SPEED       TIME       DISTANCE

FIRSTPART           r          25/r        25

SECONDPART         r+15        65/(r+15)   65

TOTAL                           1.5        90



Solve for r.

Simplification steps should lead to .






-
(Mistake made in steps done off-site --
Equation should simplify to ).
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

            The post by @josgarithmetic contains mistake and leads you to  NOWHERE.

            I came to fix his error and provide the correct solution. 


Let "r" be the speed (in miles per hours) he drove the first 25 miles; then the time to cover this distance was    hours.


The speed he drove the last 65 miles was (r+15) miles; and the time to cover this distance was    hours.


The "time" equation is  


 +  = 1.5  hours.


Multiply both sides by  2*r*(r+15)  and simplify.  You will get the quadratic equation


 = 0.


Factor left side


(r-50)*(r+5) = 0.


Of two roots, only positive root  r= 50 is meaningful.


It is your answer:  r= 50 miles per hour was the speed he drove during the first 25 miles.


CHECK.    +  =  + 1 =  hours.   ! Precisely correct !

Solved.



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