What Time Is It? Math Brainteaser (Beginning Algebra Level)

[Otis]

I just checked the wall clock and noticed that one-fifth of the time that has passed since noon is equal to one-eleventh of the time to come until noon again. What time is?

?

[imath]\;[/imath]

 

[JeffM]

Spoiler

I like this one for kids because it is easiest with a 24 hour clock starting from zero. Nice intro to relative scales, arbitrary zeroes, etc.

[math]x = \text {hours since noon today.}\\ \dfrac{x - 0}{5} = \dfrac{24 - x}{11} \implies 11x - 11 * 0 = 120 - 5x \implies\\ 16x = 120 \implies x = 7.5.[/math]
[math]\dfrac{24 - 7.5}{11} = \dfrac{16.5}{11} = 1.5 = \dfrac{7.5}{5}. \ \checkmark[/math]

 

[topsquark]

I just checked the wall clock and noticed that one-fifth of the time that has passed since noon is equal to one-eleventh of the time to come until noon again. What time is?

?

[imath]\;[/imath]

If you can see that then you can already tell time. Just read the clock!

-Dan

 

[Dr.Peterson]

I just checked the wall clock and noticed that one-fifth of the time that has passed since noon is equal to one-eleventh of the time to come until noon again. What time is?

?

I like finding non-algebraic solutions to these.

Spoiler

The total time from one noon to another is 24 hours. The time since last noon is 5 units, and the time until the next noon is 11 units, with both units having the same size. So 5+11 = 16 units is 24 hours; so 2 units is 3 hours, and 1 unit is 1.5 hours. So the time since noon is 5 times 1.5 hours, which is 7.5 hours, making the time 7:30 PM.

 

[Otis]

you can already tell time. Just read the clock!

History Teacher: What happened at the Boston Tea Party?
Student Dan: I don't know, I wasn't invited.

Civics Teacher: Which American president wore the largest hat?
Student Dan: The one with the largest head.

Science Teacher: How do you keep milk from going sour?
Student Dan: Leave it in the cow.



[imath]\;[/imath]

 

[topsquark]

History Teacher: What happened at the Boston Tea Party?
Student Dan: I don't know, I wasn't invited.

Civics Teacher: Which American president wore the largest hat?
Student Dan: The one with the largest head.

Science Teacher: How do you keep milk from going sour?
Student Dan: Leave it in the cow.



[imath]\;[/imath]

Oddly enough it was the students who were afraid of me, not the teachers!

-Dan