SOLUTION: Day 1 drive 40 miles per hour and arrive one minute late. Day 2 drive 45 miles per hour and arrive one minute early. How far do you drive to work? I know the answer is 12 mile

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Question 235957: Day 1 drive 40 miles per hour and arrive one minute late.
Day 2 drive 45 miles per hour and arrive one minute early.
How far do you drive to work?
I know the answer is 12 miles, but how do you set up the problem?
Found 3 solutions by solver91311, Stitch, ankor@dixie-net.com:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Distance equals Rate times Time, or

Notice that, since rate is given in miles per hour, time must be in hours and distance in miles.

So for the day 1 trip, the time is hours plus one minute (it took one minute longer than the hours planned). But one minute is hour, so for the fixed distance , the day 1 trip can be described:



Likewise, the day 2 trip can be described as:



Solve each of these equations for in terms of





(Verification of the two re-arrangements is left as an exercise for the student)

Now you have two expressions for in terms of , so set them equal:



And finally, solve for

John

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Since we are using two different time variables I think it is best to convert everything to one unit or the other. I am going to convert everything into minutes.
1hour = 60min
%2840miles%2F1hour%29%2A%281hour%2F60min%29+=+%28%280.6667%2Amiles%29%2Fmin%29
%2845miles%2F1hour%29%2A%281hour%2F60min%29+=+%28%280.75%2Amiles%29%2Fmin%29
In these equations X = time & Y = distance.
Equation 1: 0.6667%2A%28X%2B2%29+=+Y
The X+2 is the diffence in the arrival times. 1 minute ealry + 1minute late = 2 minutes.
Equation 2: 0.75%2AX+=+Y
Since both equations equal Y, we can set these equations equal to each other.
0.6667%2A%28X%2B2%29+=+0.75%2AX Simplify
0.6667X+%2B+1.3334+=+0.75X Subtract 0.6667X from both sides
1.3334+=+0.75X+-+0.6667X Factor out the X
1.334+=+X%2A%280.75-.06667%29 Simplify
1.334+=+X%2A%280.0833%29 Divide both sides by 0.08333
highlight%2816+=+X%29 Now we know that the time traveled was 16 minutes
Plug 16 in for X into one of the given equations
Equation 2: 0.75%2AX+=+Y
0.75%2A%2816%29+=+Y
highlight%2812+=+Y%29
Equation 1: 0.6667%2A%28X%2B2%29+=+Y
0.6667%2A%2816%2B2%29+=+Y
0.6667%2A%2818%29+=+Y
highlight%2812+=+Y%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Here is yet another way, perhaps simpler.
Day 1 drive 40 miles per hour and arrive one minute late.
Day 2 drive 45 miles per hour and arrive one minute early.
How far do you drive to work
:
Let t = time to drive to work at 45 mph
then
(t+2%2F60) = time to work at 40 mph (takes 2 min longer)
which is
(t+1%2F30)
;
The distance both days is the same, write a dist equation d = speed * time
:
day 1 dist = day 2 dist
40(t+1%2F30) = 45t
:
40t + 4%2F3 = 45t
4%2F3 = 45t - 40t
5t = 4%2F3
t = 1%2F5 * 4%2F3
t = 4%2F15 hr
:
Find the dist
45 * 4%2F15 = 12 mi