SOLUTION: one invention saves 30% on fuel; a second saves 45%;a third, 25%. if you use all three inventions at once how much can you save?

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Question 193489: one invention saves 30% on fuel; a second saves 45%;a third, 25%. if you use all three inventions at once how much can you save?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Say you used the inventions on a tank that holds
100 gallons of fuel. With the 1st invention,
you'd only use 70 gallons to go a far as you went
on a tankful before. Call that distance d mi
With the 2nd invention, you'd use 55 gallons
With the 3rd invention, you'd use 75 gallons
The fuel efficiencies are:
No inventions: d%2F100 mi/gal
1st invention: d%2F70 mi/gal
2nd invention: d%2F55 mi/gal
3rd invention: d%2F75 mi/gal
---------------------------------
These are RATES of fuel usage. I can add
the rates to get a combined rate
d%2F70+%2B+d%2F55+%2B+d%2F75
d%2A%281%2F70+%2B+1%2F55+%2B+1%2F75%29
d%2A%28165%2F11550+%2B+210%2F11550+%2B+154%2F11550%29
d%2A%28529%2F11550%29
d%2A.0458
d%2A%281%2F21.834%29
d%2A%281%2F70+%2B+1%2F55+%2B+1%2F75%29+=+d%2F21.834 mi/gal
That's how much of the 100 gallon tank
you'd use to go d mi so you would
save 100+-+21.834+=+78.166 gallons
78.166%2F100 = 78.166% saved
--------------------------------
I can check this by converting to decimals:
d%2A%281%2F70+%2B+1%2F55+%2B+1%2F75%29+=+d%2A%28.04286+%2B+.01818+%2B+.01333%29
d%2A.04579
d%2A%281%2F21.836%29
Close enough