SOLUTION: I can walk to work at 4mph or cycle at 12mph and I save ten minutes if I ride my bike. How far is it to work?

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Question 832281: I can walk to work at 4mph or cycle at 12mph and I save ten minutes if I ride my bike. How far is it to work?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Unknown variables are the time t, for walking and the distance to work, d.
Use the simple travel rate equation, R*T=D. Do not worry about the ratio of walking to cycling speeds.

______________speed________time(hours)_______distance
WALK____________4____________t_______________d
CYCLE___________12__________t-1/6____________d


Walking: 4t=d
Cycling: 12%28t-1%2F6%29=d

Simplify and try to use in the form of At+Bd=C.
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Walk equation is like 4t-d=0;
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Cycle equation, 12t-2=d
12t-d-2=0
12t-d=2

System is now useful as:
highlight_green%2812t-d=2%29 and highlight_green%284t-d=0%29
Use Elimination Method. Subtract the second equation from the first, according to the system as just shown:
12t-d-%284t-d%29=2-0
12t-d-4t%2Bd=2
12t-4t=2
6t-2t=1
4t=1
highlight%28t=1%2F4%29------A part of the answer resutl.
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Now find the distance. Use the simpler original equation for WALKING.
4t=d
4%281%2F4%29=d
1=d
highlight%28d=1%29 mile distance to work.