SOLUTION: Joel drives his car for 20 km at a certain speed. At a distance,he increases his speed by 5 km per hour and drives for an additional 20 km. If the total trip taken is 1 hour, what

Algebra ->  Pythagorean-theorem -> SOLUTION: Joel drives his car for 20 km at a certain speed. At a distance,he increases his speed by 5 km per hour and drives for an additional 20 km. If the total trip taken is 1 hour, what       Log On


   

Question 477001: Joel drives his car for 20 km at a certain speed. At a distance,he increases his speed by 5 km per hour and drives for an additional 20 km. If the total trip taken is 1 hour, what is his original speed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Joel drives his car for 20 km at a certain speed.
At a distance, he increases his speed by 5 km per hour and drives for an additional 20 km.
If the total trip taken is 1 hour, what is his original speed?
;
Let s = his original speed
then
(s+5) = his faster speed
:
Write a time equation, time = dist/speed
:
Time at original speed + time at faster speed = 1 hr
20%2Fs + 20%2F%28%28s%2B5%29%29 = 1
multiply by s(s+5) to get rid of the denominators, results:
20(s+5) + 20s = s(s+5)
20s + 100 + 20s = s^2 + 5s
40s + 100 = s^2 + 5s
combine on the right to form a quadratic equation
0 = s^2 + 5s - 40s - 100
s^2 - 35s - 100 = 0
Solve this equation using the quadratic formula
s+=+%28-%28-35%29+%2B-+sqrt%28-35%5E2-4%2A1%2A-100+%29%29%2F%282%2A1%29+
the positive solution is what you want here, check your solution in the original equation.