SOLUTION: Mary Baylor drove to work on Thursday at 40 miles per hour and arrived one minute late. She left at the same time on Friday, drove at 45 miles per hour, and arrived one minute earl
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Question 163705: Mary Baylor drove to work on Thursday at 40 miles per hour and arrived one minute late. She left at the same time on Friday, drove at 45 miles per hour, and arrived one minute early. How far does Ms. Baylor drive to work? Found 2 solutions by checkley77, gonzo:Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! D=RT
Seing as the distances are the same:
rt=rt
40(t+1/60)=45(t-1/60)
40t+40/60=45t-45/60
40t-45t=-45/60-40/60
-5t=-85/60
-5t=-17/12
t=(-17/12)/-5
t=(-17/12*-1/5)
t=17/60 travel time is 17 minutes.
Proof:
40(17+1)=40*18=720
45(17-1)=45*16=720
You can put this solution on YOUR website! let t+1 = number of minutes it took to get to work at 40 miles per hour.
let t-1 = number of minutes it took to get to work at 45 miles per hour.
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(40 * (t+1))/60 = number of miles to work.
and
(45 * (t-1))/60 = number of miles to work.
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since the speed is in miles per hour, and the time is in minutes, either the time has to be translated to hours or the speed has to be translated to miles per minute, which is why i divided by 60. one of them had to be divided by 60 to make them consistent with each other.
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since the number of miles to work is the same, then
(40*(t+1))/60 = (45*(t-1))/60
multiplying both sides of the equation by 60 to remove the denominator and it becomes
40*(t+1) = 45*(t-1)
which becomes
40t + 40 = 45t - 45
subtracting 40t from both sides of the equation and adding 45 to both sides of the equation gets
40 + 45 = 45t - 40t
which becomes
85 = 5t
which becomes
t = 17
if t = 17, then
t-1 = 16
t+1 = 18
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substituting in the original equation gets
(40*18)/60 = number of miles to work = 720/60 = 12
(45*16)/60 = number of miles to work = 720/60 = 12
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she has to drive 12 miles to get to work.
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