### Brain Teasers

# Aunt's Ol' Jalopy

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?

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

Great aunt Annie lol

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!!

Great teaser, easily solvable.

Good one.

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

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

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

Great teaser! Lots of fun.

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!

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

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

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

this is supposed to b a brain teaser! not homework!

Ah, I shoud have read the question throughly.

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

My head started spinning after the first sentence.

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

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

Should it not be 20/30 to find gallons per hour??

Thanks

Thanks

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.

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.

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

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