A question bugging me: John takes 2.5 hours to assemble 450 puzzle pieces and 3.5 hours to assemble 650 puzzle pieces.

[juh]

Don't have any pictures but I remember some important details. John takes 2.5 hours to assemble 450 puzzle pieces and 3.5 hours to assemble 650 puzzle pieces. The growth is constant, create a linear equation with "y" as the amount of hours it takes and "x" as the amount of puzzle pieces. I need help with figuring out this equation.

 

[stapel]

Don't have any pictures but I remember some important details. John takes 2.5 hours to assemble 450 puzzle pieces and 3.5 hours to assemble 650 puzzle pieces. The growth is constant, create a linear equation with "y" as the amount of hours it takes and "x" as the amount of puzzle pieces. I need help with figuring out this equation.

You've been given two data points, (pieces, hours). You've been told that these points lie on a straight line. So apply the straight-line stuff you've learned (like finding slope) to determine the equation.

If you get stuck, please reply with a clear listing of your thoughts and efforts so far. Thank you!

Eliz.

 

[Steven G]

This problem makes no sense as it should cross the origin, however the h intercept is not 0. This means that if the number of pieces for a puzzle is 0, then it would NOT take 0 hours to assemble this puzzle with 0 pieces!!!!

 

[juh]

I realized this during my test and it confused me a lot but I guess it's just bad question design. Maybe it takes time to get the pieces out or something but if there are no pieces then this wouldn't make sense. This was a question on a state algebra 1 test.

 

[juh]

You've been given two data points, (pieces, hours). You've been told that these points lie on a straight line. So apply the straight-line stuff you've learned (like finding slope) to determine the equation.

If you get stuck, please reply with a clear listing of your thoughts and efforts so far. Thank you!

El

Feels good

 

[khansaheb]

W

Don't have any pictures but I remember some important details. John takes 2.5 hours to assemble 450 puzzle pieces and 3.5 hours to assemble 650 puzzle pieces. The growth is constant, create a linear equation with "y" as the amount of hours it takes and "x" as the amount of puzzle pieces. I need help with figuring out this equation.

What is the equation of a line passing through (x₁ , y₁) and (x₂ , y₂) ?

Look up in your text-book.

 

[Steven G]

W

What is the equation of a line passing through (x₁ , y₁) and (x₂ , y₂) ?

Look up in your text-book.

What you and @stapel are suggesting is the only way to do this problem just doesn't feel right. How can it take a non-zero (including negative values!) length of time to assemble a puzzle that has zero pieces?
A situation like this, imo, must be proportional (ie cross the origin) and this setup is not.

 

[khansaheb]

What you and @staple are suggesting is the only way to do this problem however it just doesn't feel right. How can it take a non-zero (including negative values!) length of time to assemble a puzzle that has zero pieces?
A situation like this, imo, must be proportional (ie cross the origin) and this setup is not.

You could restrict the domain [250, 650]

 

[Steven G]

To OP, could the 650 have in fact been 630?

 

[Steven G]

You could restrict the domain [250, 650]

Fine, but that doesn't eliminate the fact that the given points are not proportional.

Here is exactly what I am saying:
You can do a 450 piece puzzle in 2.5 hrs. That means that you can do 180 pieces in 1 hour. So in 3.5 hours you should be able to finish a 630 piece puzzle--Not a 650 piece puzzle.

I guess as time goes by one can do more pieces per hour but that is against this situation being linear as two helpers suggested and one of them is a very long time member.

 

[juh]

Fine, but that doesn't eliminate the fact that the given points are not proportional.

Here is exactly what I am saying:
You can do a 450 piece puzzle in 2.5 hrs. That means that you can do 180 pieces in 1 hour. So in 3.5 hours you should be able to finish a 630 piece puzzle--Not a 650 piece puzzle.

I guess as time goes by one can do more pieces per hour but that is against this situation being linear as two helpers suggested and one of them is a very long time member.

It was 650 pieces I'm almost fully sure. Technically the math works but just not in a practical way. Probably just bad question design again. I'm like 98% sure on all the numbers in the question and that the growth rate is constant. Thanks for the help!