Aunt's Ol' Jalopy
Math brain teasers require computations to solve.
After visiting my Great Aunt Annie, I travelled home in her old jalopy. The car was old and battered, it had a leak from the petrol tank, and I was stuck in second gear.
This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel.
At the start of the journey I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour.
Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.
How far was it from my Great Aunt's to my home?
Answer
150 miles.
I was travelling at 30mph at a rate of 20mpg, so I was using 1.5 gallons every hour for the driving itself. I was also losing 0.5 gallon every hour, so in total, I was using 2 gallons every hour. Therefore to use all of the 10 gallons I started with, I travelled for 5 hours.
5 hours at 30mph is 150 miles.
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Comments
Melanmel16
Mar 28, 2012
 Great aunt Annie lol 
Babe
Apr 24, 2012
 I did not even try. Did not like math in school and certainly was not going to bust my brain on this one. How about a real quiz that doesn't take us back to the class room!! 
HABS2933
Apr 24, 2012
 Great teaser, easily solvable. 
bestgirl
Apr 24, 2012
 Good one. 
dsjt
Apr 24, 2012
 Where did your aunt find a "jalopy" that jets 20 MPG? I wished my vehicle could get that. 
xdbtcp
Apr 24, 2012
 I figured 20 miles per gallon, and you had 10 gallons, so you went 200 miles... 
xdbtcp
Apr 24, 2012
 Guess I shoulda read "the fuel tank lost fuel at the rate of half a gallon per hour." 
gghali
Apr 24, 2012
 Great teaser! Lots of fun. 
wordmama
Apr 24, 2012
 I love math, even though it's not my field. I wanted to try it, but I couldn't figure out how to reconcile the mpg, the mph, and the fuel loss. The explanation was excellent; I'm disappointed in myself that I couldn't see it on my own! 
FatHead
Apr 24, 2012
 That was awesome. I'm glad I had as much practice as I did with highschool algebra and word problems. 
bradon182001
Apr 24, 2012
 Nice teaser, never hurts to practice a little math to keep the mind active. 
auntiesis
Apr 24, 2012
 I love math problems, but this one was way too easy. But I still loved it. 
luluw5
Apr 24, 2012
 this is supposed to b a brain teaser! not homework! 
DarylK
May 25, 2012
 Ah, I shoud have read the question throughly. 
Babe
Apr 24, 2015
 I suggest you get the car fixed immediately for your Aunt as leaking fuel can be very dangerous! 
catmom
Apr 24, 2015
 My head started spinning after the first sentence. 
xdbtcp
Apr 24, 2015
 I figured 20 miles per gallon, and you had 10 gallons, so you went 200 miles... 
xdbtcp
Apr 24, 2015
 Guess I shoulda read "the fuel tank lost fuel at the rate of half a gallon per hour." 
shaswot
Nov 18, 2015
 Should it not be 20/30 to find gallons per hour??
Thanks 
Paladin
Feb 25, 2016
 I'm a fan of algebra, so I solved this differently:
The total distance (d) is represented by 30t (30 MPH x hours travelled)
d = 30t
Also the total distance travelled is (20MPG * 10 gallons)  (0.5 gallons * 20 MPG * t)
d = 200  10t
Set these equal and solve for t:
30t = 200  10t
40t = 200
t = 5 hours
5 hours at 30 MPH = 150 miles
Not as simple as the given solution, but certainly more universal ;)
Nice teaser. 
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