Math question, not sure where to ask this, possible explaining help?

[Galadriel]

Hi there
I am re-learning some math (on my own, no teacher or tutor), and having trouble understanding how they got the correct answers to this question. I've been looking all around the internet for similar problems with explanation, but not finding it. This is a question given on Khan Academy.

The question is: Rob spent 25% more time on his research project than he had planned. He spent an extra h hours on the project. Which two below represent the hours actually spent on it?

a) 4h
b) (1 + 25/100)h
c) 1.25h
d) 5h
e) (h/0.25)1.25

It gives the correct answers as choice d and e.

So h is the extra hours spent on the project.

In the explanation given, it sets it up as planned to spend h/25% hours, and actually spent is h/25% + h hours. I do not understand why h is divided by 25%. Wouldn't it be 25% of the hours planned plus the extra h hours to get total hours spent on the project? That would be set up as .25(hours planned) + h. This obviously is not correct though. I feel stupid for not getting this but it is really stumping me. Anyone able to give clarification?

 

[Residential Bob]

42

 

[Sabertooth]

While the OP is true, it seems quite convoluted.

Let t = the amount of time he intended to spend on the project.
He actually spent

• 1t + 0.25t =
• (1 + 0.25)t =
• 1.25t

h = 0.25t, so

• xh = 1.25t
• x = 1.25t/h =
  
• 1.25t/0.25t =
• 5 * 0.25t/0.25t =
• 5

Therefore, 1.25t = 5h

 

[devin553344]

Hi there
I am re-learning some math (on my own, no teacher or tutor), and having trouble understanding how they got the correct answers to this question. I've been looking all around the internet for similar problems with explanation, but not finding it. This is a question given on Khan Academy.

The question is: Rob spent 25% more time on his research project than he had planned. He spent an extra h hours on the project. Which two below represent the hours actually spent on it?

a) 4h
b) (1 + 25/100)h
c) 1.25h
d) 5h
e) (h/0.25)1.25

It gives the correct answers as choice d and e.

So h is the extra hours spent on the project.

In the explanation given, it sets it up as planned to spend h/25% hours, and actually spent is h/25% + h hours. I do not understand why h is divided by 25%. Wouldn't it be 25% of the hours planned plus the extra h hours to get total hours spent on the project? That would be set up as .25(hours planned) + h. This obviously is not correct though. I feel stupid for not getting this but it is really stumping me. Anyone able to give clarification?

oops. I believe that answer is d or 5h. Dividing h by 0.25 gives a growth factor of 4 which is h/0.25 or h*1/0.25 then multiplying times 1.25 yields 5h again

 

[usexpat97]

Try it with some hard numbers. He planned to spend 4 hours. He spent 25% more than planned, which is 5. H is 1.

 

[Porpoise]

The question is: Rob spent 25% more time on his research project than he had planned. He spent an extra h hours on the project. Which two below represent the hours actually spent on it?

When I first looked at this I assumed h was the hours he planned to spend on it, so I was confused at first. Then I noticed it says "he spent an extra h hours". So h is not the hours planned but the extra hours, which means h is .25 (of the time he planned to spend). The actual amount of time spent is 1.25 of the planned hours.

d) 5h -----------> 5 (.25) = 1.25
e) (h/0.25)1.25 ------------> .25 / .25 * 1.25 = 1 * 1.25 = 1.25

 

[Sabertooth]

Answer e is just a more convoluted expression of answer d.

 

[usexpat97]

Certainly, but you can eyeball it: 4h x 1.25 = 5h.

 

[paul1149]

I do not understand why h is divided by 25%.

I also find this convoluted, but the way they got h/.25 is:

• h = .25t
• h/.25 = t (divide both sides by .25 to solve for t )

 

[JackRT]

While the OP true, it seems quite convoluted.

Let t = the amount of time he intended to spend on the project.
He actually spent

• 1t + 0.25t =
• (1 + 0.25)t =
• 1.25t

h = 0.25t, so

• xh = 1.25t
• x = 1.25t/h =
  
• 1.25t/0.25t =
• 5 * 0.25t/0.25t =
• 5

Therefore, 1.25t = 5h

Perfect!!!

 

[usexpat97]

But is this more convoluted than real life? Make it an oddball number, 42%.

If h= the 42%, then you have to divide by .42 to get how much he thought he would spend. That's h/.42 . (h/.42)(1.42) would be it. Although I think (h/.42)+h is simpler. A little algebra will prove the two are the same.

 

[icxn]

If 25% is h then 100% is 4h. Add the extra h and you get a total of 5h spent. Also 1.25/0.25 = 5 so options d and e.

 

[Galadriel]

Thank you for the help! I will have to study your answers. It is a really oddball way of doing it isn't it? I think that was throwing me off so much, couldn't get from the logical way to the convoluted way they had it in the answers.