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Aunt's Ol' Jalopy

Math brain teasers require computations to solve.


Puzzle ID:#49384
Fun:*** (3.06)
Difficulty:** (1.59)
Submitted By:firefox99Aus******




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?

Open Calculator


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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Mar 28, 2012

Great aunt Annie lol
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!!
Apr 24, 2012

Great teaser, easily solvable.
Apr 24, 2012

Good one.
Apr 24, 2012

Where did your aunt find a "jalopy" that jets 20 MPG? I wished my vehicle could get that.
Apr 24, 2012

I figured 20 miles per gallon, and you had 10 gallons, so you went 200 miles...
Apr 24, 2012

Guess I shoulda read "the fuel tank lost fuel at the rate of half a gallon per hour."
Apr 24, 2012

Great teaser! Lots of fun.
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!
Apr 24, 2012

That was awesome. I'm glad I had as much practice as I did with high-school algebra and word problems.
Apr 24, 2012

Nice teaser, never hurts to practice a little math to keep the mind active.
Apr 24, 2012

I love math problems, but this one was way too easy. But I still loved it.
Apr 24, 2012

this is supposed to b a brain teaser! not homework!
May 25, 2012

Ah, I shoud have read the question throughly.
Apr 24, 2015

I suggest you get the car fixed immediately for your Aunt as leaking fuel can be very dangerous!
Apr 24, 2015

My head started spinning after the first sentence.
Apr 24, 2015

I figured 20 miles per gallon, and you had 10 gallons, so you went 200 miles...
Apr 24, 2015

Guess I shoulda read "the fuel tank lost fuel at the rate of half a gallon per hour."
Nov 18, 2015

Should it not be 20/30 to find gallons per hour??
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.
Oct 08, 2016

Fun teaser. Thanks for posting it - and how about a few more, Firefox?

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