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Aunt's Ol' Jalopy

Math brain teasers require computations to solve.

 

Puzzle ID:#49384
Fun:*** (3.06)
Difficulty:** (1.59)
Category:Math
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?

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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

Melanmel16us*
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!!
HABS2933Aca*
Apr 24, 2012

Great teaser, easily solvable.
bestgirl*
Apr 24, 2012

Good one.
dsjtus*
Apr 24, 2012

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

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

That was awesome. I'm glad I had as much practice as I did with high-school algebra and word problems.
bradon182001*us*
Apr 24, 2012

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

I love math problems, but this one was way too easy. But I still loved it.
luluw5*us*
Apr 24, 2012

this is supposed to b a brain teaser! not homework!
DarylKca*
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!
catmomAus*
Apr 24, 2015

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

I figured 20 miles per gallon, and you had 10 gallons, so you went 200 miles...
xdbtcpAus**
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
PaladinAus*
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.
dalfamnestAnz*
Oct 08, 2016

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

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