Fun math problem that stumps everyone

[f35phixer]

a new one...

After a long day of work, I was relieved. I had been working since 4pm in a circuitry lab, working on the next big project. I observed the sun just starting to descend as I started to walk out to my car. All of a sudden, however, I had an urge to sneeze furiously! If it's the middle of January on a windy day, what's happening here?

 

[Car-Guy]

^^^^^^Somethings just don't makes sense in the above riddle but I'll still guess the reason for sneezing is a "sensitivity to sunlight".

 

[Out-to-Lunch]

If the sun is "starting to descend" after midnight in January, you must be in southern Chile, and you suffer from seasonal allergies?

 

[Koolau]

Yup, high school physics. And more teachers should use drills like this because it relates well to what teenage boys like - fast cars.

My fav; a car accelerates at 1G constant. What's the quarter mile time and the speed through the traps?

Hint, this is a fast car -

Yeah, and if the physics teacher could somehow relate the answer to HS girls, it would be even better.

"Sally, the prettiest cheerleader in the whole Senior class will only date the guy with the fastest car in the school. Ralph's Camaro accelerates at 1G constant. Is it likely Sally will go out with Ralph after watching him at the local drags? If so, why? How fast will Ralph's car be traveling at the end of the quarter mile and what is his ET?"

 

[Koolau]

^^^^^^Somethings just don't makes sense in the above riddle but I'll still guess the reason for sneezing is a "sensitivity to sunlight".

I did know a guy who, each time he walked out of a building into sunlight, he would sneeze 3 or 4 times. Some sources suggest that a significant minority of the population suffers from photic sneeze reflex though I only knew the one guy for which is was so obvious. YMMV

 

[Car-Guy]

^^^^^
Yep, I knew a guy like that too...

 

[RunningBum]

That's me. 3 sneezes. Not 2, not 4. But it doesn't happen as regularly as it used to. Maybe I'm more likely to have sunglasses on before hitting the sun. Or maybe it still happens and I don't even notice anymore.

 

[Koolau]

No a Challenger/Hellcat

This site https://www.zeroto60times.com/vehicle-make/tesla-0-60-mph-times/ lists several Tesla models that can beat the Challenger/Hellcat in 0 to 60 times. Didn't even check 1/4 mile times on the Hellcat as that's not an EV's strong suit though YMMV.

Would love to ride in a Tesla with Ludicrous some day (but I'd settle for a Challenger/Hellcat.) BFF (the one half a mil in debt at 77) has his Vette down into the 9's in the quarter. No idea what 0 to 60 would be.

Ahh, suddenly I'm hearing this mental tape playing US30 Drag Strip commercials on WLS, The Rock Of Chicago. How do I turn it off?

 

[Car-Guy]

This site https://www.zeroto60times.com/vehicle-make/tesla-0-60-mph-times/ lists several Tesla models that can beat the Challenger/Hellcat in 0 to 60 times. Didn't even check 1/4 mile times on the Hellcat as that's not an EV's strong suit though YMMV.

Would love to ride in a Tesla with Ludicrous some day (but I'd settle for a Challenger/Hellcat.) BFF (the one half a mil in debt at 77) has his Vette down into the 9's in the quarter. No idea what 0 to 60 would be.

Ahh, suddenly I'm hearing this mental tape playing US30 Drag Strip commercials on WLS, The Rock Of Chicago. How do I turn it off?

It's extremely difficult for any street legal RWD performance car to break 3sec in a 0-60 run. (Traction issues) Mid to upper 3's can be done but that takes some practice. I've read that the new RWD C8 Corvette can do it (just) but that's becasue it has a new mid engine design. (weight distribution) And of course the limited production Dodge Demon that can hit 60 in the low 2's. However there are a few street legal high performance AWD cars that can break 3 secs. In anycase after 40 to 60mph, RWD's vehicles "typically" regain the advantage. An EV like the 1020hp Tesla S/Plaid are a different animal since they not only have AWD but they have multiple drive motors.

 

[leftyfrizzell1963]

Ok. I take it this way. Driver traveled at 30 mph in the first mile. Let's assume that is the average.

So that means his/her speed at the end of the first mile is 60 mph since the starting speed is 0 mph.

Problem states that the driver averages 60 mph over 2 miles. Since the driver averaged 30 mph in the first mile, he/she needs to average 90 mph in the 2nd mile in order to average 60 mph for the whole 2 miles. (30 ave mph mile 1 + 90 mph ave mile 2) / 2.

Since the driver was driving 60 mph at the beginning of mile 2, the driver needs to get going 120 mph at the end of mile 2 to average 90 mph in the 2nd mile.

The answer is 120 mph.

I saw several references to a 2 minute limit in the replies, and therefore its impossible. I saw no 2 minute limitation or any time limitation in the OP original problem statement. The 1st sentence says "travel at a speed of 30mph". MPH is by far the most common way we measure a 'rate of speed'. Since it is measurable, we can do the math. I see no reason to impose a 2 minute time limit in the problem statement.

I've read through this whole thread, and this above is the only real answer based on practical physical capabilities of a car/rocket/airplane/object/person/thing/X/etc. My answer would be 90 if an object could go from 30 to 90 instantaneously. However, I change my answer to 120 based on general physical properties.

 

[ERD50]

I did know a guy who, each time he walked out of a building into sunlight, he would sneeze 3 or 4 times. Some sources suggest that a significant minority of the population suffers from photic sneeze reflex though I only knew the one guy for which is was so obvious. YMMV

That's me. 3 sneezes. Not 2, not 4. But it doesn't happen as regularly as it used to. Maybe I'm more likely to have sunglasses on before hitting the sun. Or maybe it still happens and I don't even notice anymore.

I didn't know that was a "thing", but I have it. Almost always 3 sneezes. Rarely less.

DW talks about looking at a light to get a sneeze out, I guess that is a thing, don't think I ever tried it.


But please, if no tissue handy, sneeze into your elbow, not your bare hands (gross!))

-ERD50

 

[ERD50]

Originally Posted by Ronstar View Post
Ok. I take it this way. Driver traveled at 30 mph in the first mile. Let's assume that is the average.

So that means his/her speed at the end of the first mile is 60 mph since the starting speed is 0 mph.

Problem states that the driver averages 60 mph over 2 miles. Since the driver averaged 30 mph in the first mile, he/she needs to average 90 mph in the 2nd mile in order to average 60 mph for the whole 2 miles. (30 ave mph mile 1 + 90 mph ave mile 2) / 2.

Since the driver was driving 60 mph at the beginning of mile 2, the driver needs to get going 120 mph at the end of mile 2 to average 90 mph in the 2nd mile.

The answer is 120 mph.

I saw several references to a 2 minute limit in the replies, and therefore its impossible. I saw no 2 minute limitation or any time limitation in the OP original problem statement. The 1st sentence says "travel at a speed of 30mph". MPH is by far the most common way we measure a 'rate of speed'. Since it is measurable, we can do the math. I see no reason to impose a 2 minute time limit in the problem statement.

I've read through this whole thread, and this above is the only real answer based on practical physical capabilities of a car/rocket/airplane/object/person/thing/X/etc. My answer would be 90 if an object could go from 30 to 90 instantaneously. However, I change my answer to 120 based on general physical properties.

No, that's very wrong.

The 2 minute limit is there, but not spelled out as such. Here's the OP:

If you travel at a speed of 30mph in the 1st mile, how fast do you have to go in the second mile so you have an average speed of 60mph over the 2 mile stretch?

If you average 60 mph over 2 miles, that is 2 minutes, no more no less.

60 mph is conveniently "a mile a minute". So two miles at a mile a minute is two minutes.

There's your 2 minute limit.

PS: just noticed your screen name, so maybe this vehicular speed problem gave you the "Travelin' Blues"? Your calculations could make you "Always Late", so "Before You Go (Be Sure You Know)". Otherwise, it might take you "Forever (And Always)" to get there, and people will tell you "You're Too Late".

-ERD50

 

[NW-Bound]

I did not know this singer, so had to look him up.

Here's "Travelin' Blues" by Lefty Frizzell.

 

[Koolau]

Poor Lefty. Another mega-talent who couldn't deal with the fame and other trappings of celebrity. He died at 47 from the effects of alcoholism. Tragedy seems rife in the country music world - just as in other forms of popular music. Returning you now...

 

[freedom2022]

I was at the front line of the red right. This car stopped beside mine and the driver started to roar his muffler. I let him off and tried to surpass him one second later. I was not successful.
So, I came to think another interesting HS physics question.
I searched the acceleration speed of his car: 0 - 60 in 7 sec.
Mine takes 6 sec. Why I could not catch him?

 

[f35phixer]

a new one...

After a long day of work, I was relieved. I had been working since 4pm in a circuitry lab, working on the next big project. I observed the sun just starting to descend as I started to walk out to my car. All of a sudden, however, I had an urge to sneeze furiously! If it's the middle of January on a windy day, what's happening here?

Sorry been offline for a bit
Photic Sneeze Syndrome……

 

[f35phixer]

new one arrrraghhhhh. it beat me ;-)

What phrase is represented by the following?

Look kool XtXhXeXrXoXaXdX

 

[ERD50]

new one arrrraghhhhh. it beat me ;-)

What phrase is represented by the following?

Look kool XtXhXeXrXoXaXdX

Spoiler alert - white text:

Look both ways before you cross the road.

Not really a math problem. - ERD50

 

[f35phixer]

but still made your brain work, correctly by the way ;-)

 

[Out-to-Lunch]

Sorry been offline for a bit
Photic Sneeze Syndrome……

If the sun is "starting to descend" after midnight in January, you must be in southern Chile, and you suffer from seasonal allergies?

Okay, I understand you threw in lots of red herrings, but what about that whole "sun starting to descend" in January some time after midnight bit?

 

[f35phixer]

Two 2s can be combined in many ways to express different numbers. Here are some!
2-2=0
2/2 = 1
.2 + 2 = 2.2
(2^2)! = 24 (4! means 4x3x2x1) (2^2 is 2 to the power of 2)

**CHALLENGE!**
Can you write an expression that has the value of exactly 5, using:
* two, and only two, 2s, and
* any mathematical symbols or operations?

You may not use any other numbers. The symbols used would be known by most high school maths students.

 

[Philliefan33]

Spoiler (scroll down for answer)















(2^2) + (2/2) = 5

 

[dheb]

Can you write an expression that has the value of exactly 5, using:
* two, and only two, 2s, and
* any mathematical symbols or operations?

You may not use any other numbers. The symbols used would be known by most high school maths students.

That depends .. do you count an exponent that squares a number to be a "2" in the expression, or not?

 

[Philliefan33]

Oh never mind, I just saw that I can only use two 2’s. Let me think on this

 

[Out-to-Lunch]

Two 2s can be combined in many ways to express different numbers. Here are some!
2-2=0
2/2 = 1
.2 + 2 = 2.2
(2^2)! = 24 (4! means 4x3x2x1) (2^2 is 2 to the power of 2)

**CHALLENGE!**
Can you write an expression that has the value of exactly 5, using:
* two, and only two, 2s, and
* any mathematical symbols or operations?

You may not use any other numbers. The symbols used would be known by most high school maths students.

SUM(k<=2) [k^2] ?

EDIT: I changed my summation variable to "k" from "i" to avoid confusion with my next entry.