SOLUTION: Praying that someone out there can help me assist my daughter with this problem. Two girls went on a run. Cary began running 40 seconds earlier than Kristie. *Cary ran at a

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Question 972881: Praying that someone out there can help me assist my daughter with this problem.
Two girls went on a run. Cary began running 40 seconds earlier than Kristie.
*Cary ran at a speed of 10 feet per second
*Kristie ran at a speed of 12 feet per second
For how many seconds had Cary been running at the moment when the two girls had ran exactly the same distance.
This problem falls under "Linear equations and proportions."
Any feedback would be greatly appreciated.
Thanks in advance.
Found 2 solutions by macston, MathTherapy:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
distance=rate x time
Since distance is the same:
Carey's rate x Carey's time=Kristie's rate x (Carey's time - 40 seconds)
Let T=Carey's time
(10ft/s)(T)=(12ft/s)(T-40s)
(10ft/s)T=(12ft/s)T-480ft Subtract (12ft/s)T from each side.
(-2ft/s)T=-480ft Divide each side by (-2ft/sec)
T=240s Carey's time when both girls had run the same distance was 240 seconds.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Praying that someone out there can help me assist my daughter with this problem.
Two girls went on a run. Cary began running 40 seconds earlier than Kristie.
*Cary ran at a speed of 10 feet per second
*Kristie ran at a speed of 12 feet per second
For how many seconds had Cary been running at the moment when the two girls had ran exactly the same distance.
This problem falls under "Linear equations and proportions."
Any feedback would be greatly appreciated.
Thanks in advance.
Let time it would take Cary to get to “meeting point” be T

Then time it would take Kristie to get to “meeting point” is: T – 40

Distance covered by Cary when they meet: 10T

Distance covered by Kristie when they meet: 12(T – 40), or 12T – 480

When they meet, they would cover the same distance

Therefore, we get: 10T = 12T – 480

10T – 12T = - 480 

– 2T = - 480

T, or time Cary would take to get to “meeting point” = %28-+480%29%2F%28-+2%29, or highlight_green%28system%28240_secs_or%2C4_mins%29%29