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

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Question 162021: Joel drives his car for 20km at a certain speed.At a distance,he increases his speed by 5 km per hour and drives for an additional 20km.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 20km at a certain speed; he increases his speed by 5 km
per hour and drives for an additional 20km. If the total trip taken.
is 1 hour, what is his original speed?
:
Let s = his original speed
then
(s+5) = his increased speed
:
Write a time equation; Time = dist%2Fspeed
;
Orig speed time + increase speed time = 1 hour
20%2Fs + 20%2F%28%28s%2B5%29%29 = 1
;
Multiply equation by s(s+5), results;
20(s+5) + 20s = s(s+5)
:
20s + 100 + 20x = s^2 + 5s
40s + 100 = s^2 + 5s
:
0 = s^2 + 5s - 40s - 100
A quadratic equation:
s^2 - 35s - 100 = 0
Solve this with the quadratic formula;
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this problem: a=1, b=-35, c=-100
s+=+%28-%28-35%29+%2B-+sqrt%28-35%5E2+-+4%2A1%2A-100+%29%29%2F%282%2A1%29+
s+=+%2835+%2B-+sqrt%281225+%2B+400+%29%29%2F%282%29+
Do the math here, the positive solution should be:
s = 37.656 km/hr is the original speed
;
:
Check solution on a calc:
20/37.656 + 20/42.656 = .99998 ~ 1