SOLUTION: On the 42 km go kart course Arshia drives .4 km/hr faster than Sarah, but she has engine trouble part way around the track and has to stop to get the cart fixed. This stop costs A

Algebra ->  Equations -> SOLUTION: On the 42 km go kart course Arshia drives .4 km/hr faster than Sarah, but she has engine trouble part way around the track and has to stop to get the cart fixed. This stop costs A      Log On


   

Question 255014: On the 42 km go kart course Arshia drives .4 km/hr faster than Sarah, but she has engine trouble part way around the track and has to stop to get the cart fixed. This stop costs Arshia one half hour, and so she arrives 15 minutes after Sarah at the end of the course. How fast did each girl drive and how long did each girl take to finish the course? I think that Sarah drove 52.5 km/hour and finished the course in 48 minutes. I then think that Arshia drove 52.9 km/h and took 63 mins to complete the course. I really am hoping that this correct and could certainly use some help if not. Thanks so much for your time.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
On the 42 km go kart course Arshia drives .4 km/hr faster than Sarah, but she has engine trouble part way around the track and has to stop to get the cart fixed.
This stop costs Arshia one half hour, and so she arrives 15 minutes after Sarah at the end of the course.
How fast did each girl drive and how long did each girl take to finish the course?
:
I am not sure how you did this, but here's my take on it:
:
Change 15 min to .25 hr
:
Let s = Sarah's speed
then
(s+.4) = Arshia's speed
:
42%2Fs = S's travel time
then
+ .25 = 42%2F%28%28s%2B.4%29%29 + .5
:
42%2Fs = 42%2F%28%28s%2B.4%29%29 + .5 - .25
:
42%2Fs = 42%2F%28%28s%2B.4%29%29 + .25
Multiply by s(s+.4), results
42(s+.4) = 42s + .25s(s+.4)
:
42s + 16.8 = 42s + .25s^2 + .1s
:
Arrange as a quadratic equation
.25s^2 + .1s + 42s - 42s - 16.8 = 0
.25s^2 + .1s - 16.8 = 0
:
Multiply by 20, get rid of those decimals
5s^2 + 2s - 336 = 0
:
Factor this to
(5s + 42)(s-8) = 0
:
positive solution
s = 8 km/h is Sarah's speed
and
8.4 km/h is Arshia's speed
;
:
Find the times of each:
42/8 = 5.25 hrs
42/8.4 = 5 hrs, + .5 = 5.5 hrs (checks out, 15 min after Sarah)