### 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?

It took me a little time, but I'm glad I got it!

I started doing this, but I really am not a fan of math problems and gave up after a short time. I agree with Babe, you should get Auntie's car fixed for her!

When it was posted in 2012 it got 12 (TWELVE) comments.

Now it gets two. And new teasers get nothing.

Does anybody care?

Braingle is suffering.

Check the TOTD of yesterday for how we can fix it.

Jaye

Now it gets two. And new teasers get nothing.

Does anybody care?

Braingle is suffering.

Check the TOTD of yesterday for how we can fix it.

Jaye

I tried but I did not get this one; I was always good in math but I have been out of school too long and my math skills are very rusty.

This is a terrific simple (that is relative...) algebra word problem. I did it in my head pretty quickly, but I have a masters in applied mathematics, so...

I really like the way it incorporates different facts: MPG, MPH, and fuel leak rate. It is a logic problem almost more than a math problem. Determining the strategy to solve (find gallons per hour, find total time, then find total distance) is the real puzzle.

I really like the way it incorporates different facts: MPG, MPH, and fuel leak rate. It is a logic problem almost more than a math problem. Determining the strategy to solve (find gallons per hour, find total time, then find total distance) is the real puzzle.

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