SOLUTION: On a 42km go-kart course, Arshia drives 0.4km/hr faster than Sarah, but has engine trouble and stops for 30min. Arshia arrives at the finish line 15min after Sarah. How fast did ea

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Question 519177: On a 42km go-kart course, Arshia drives 0.4km/hr faster than Sarah, but has engine trouble and stops for 30min. Arshia arrives at the finish line 15min after Sarah. How fast did each girl drive and how long did each girl take to finish the course?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
On a 42km go-kart course, A drives 0.4km/hr faster than S, but has engine trouble and stops for 30min.
A arrives at the finish line 15min after S.
How fast did each drive and how long did each take to finish the course?
:
Let s = S's speed
then
(s+.4) = A's speed
:
Change 30 min to .5 hrs
Change 15 min to .25 hrs
:
Write a time equation, time = dist/speed
:
A's time = S's time + .25 hr
42%2F%28%28s%2B.4%29%29 + .5 = 42%2Fs + .25
42%2F%28%28s%2B.4%29%29 = 42%2Fs + .25 -.5
42%2F%28%28s%2B.4%29%29 = 42%2Fs - .25
:
multiply by s(s+.4), results:
42s = 42(s+.4) - .25s(s+.4)
42s = 42s + 16.8 - .25s^2 - .1s
:
Combine like terms on the left
.25s^2 + .1s + 42s - 42s - 16.8 = 0
.25s^2 + .1s - 16.8 = 0
;
Get rid of those decimals, multiply by 100
25s^2 + 10s - 1680 = 0
:
simplify, divide by 5
5s^2 + 2s - 336 = 0
:
you can use the quadratic formula to solve, but this will factor to:
(5s+42)(s-8) = 0
:
Positive solution is what we want here
s = 8 km/hr is S's speed
then, obviously,
8.4 km/h is A's speed
:
:
:
See if that work out
42%2F8.4 + .5 = 42%2F8 + .25
5 + .5 = 5.25 + .25
5.5 = 5.5; confirms our solutions