1. ## Algebra and percentages - In need of helpful hints

Hi everyone, I have a homework question which I don't know how to answer. Here is the question:

Harry is walking in a marathon. He was intending to complete the marathons total distance of 42km in seven hours while keeping a steady pace of 6km per hour. He was going good for his first four hours but developed a cramp in his legs and stopped to rest for 18 minutes. By what percentage will he need to increase his walking speed for the rest of the marathon if he is still going to complete it in seven hours? Include steps to your answer.

Now, I'm not sure how to calculate this. I subtracted 18 from the last 3 hours of the marathon and got 2 hours and 42 minutes. I then converted this to a decimal (2.7) and then to a percentage (38.6 2s.f) but I'm not sure I'm on the right track. Another problem is that I'm supposed to incorporate algebra into my answer and I have no idea how to do so. Anybody willing to help me out and confirm whether I'm correct or not on my earlier calculation? Thanks all.

2. ## Re: Algebra and percentages - In need of helpful hints

Hi there,

So, we have the distance he covered during the first 4 hours, find the distance that has to be covered, which you can calculate in meters 42000 - (4*6000) = 42 000 - 24 000 = 18000m

The speed would be more confortable to be calculated as m/min, which gives you 6km/hr = 6000m/60min = 100m

He is left with 2hr42 min, or 162min - get now the speed with which he needs to cover those 18000m;

The percentage you can evaluate in the end, hope this helps,

3. ## Re: Algebra and percentages - In need of helpful hints

Hi there, thanks a lot for your reply! I think I'm beginning to understand a bit better now
So, I think I figured out the speed by using the calculator: 6.66667km per hour

Though I should round this to the nearest significant figure: 6.7km per hour. Please feel free to correct me if I am wrong, I need all the help I can get haha. Thanks again!

4. ## Re: Algebra and percentages - In need of helpful hints

looks good, crystuls!

5. ## Re: Algebra and percentages - In need of helpful hints

...and don't forget to express in percentage the increase you got

6. ## Re: Algebra and percentages - In need of helpful hints

I'm not sure i understand what the speed is (I'm pretty slow, sorry). What is the increase and how do I calculate this to a percentage?

edit: so was my percentage correct in my first post? The percentage is 38.6%?

7. ## Re: Algebra and percentages - In need of helpful hints

...but you already have the answer: the initial speed is 6km per hour, for the second part you have got ... 6.7km per hour, isn't it?

so, what's the increase, and how can it be expressed in %...

8. ## Re: Algebra and percentages - In need of helpful hints

Ah! The increase from 6km/hour to 6.7km/hour is 0.7km, yes? 6 + 0.7 = 6.7

9. ## Re: Algebra and percentages - In need of helpful hints

yes, and what's the value of 0.7 increase, expressed in percentage?

70%?

11. ## Re: Algebra and percentages - In need of helpful hints

Originally Posted by Crystuls
70%?
you have 6km/h, which is considered 100%
and 0.7km/h, which is x %

how is that 70%???

12. ## Re: Algebra and percentages - In need of helpful hints

Hmm..8.6% (1 s.f) ???

i got this by: 6 divided by 0.7 = 8.5714 so I just rounded it to 8.6

13. ## Re: Algebra and percentages - In need of helpful hints

%$\displaystyle = \frac{.7}{6}(100)$

14. ## Re: Algebra and percentages - In need of helpful hints

Are you sure? ....(0,7 * 100)/6...

15. ## Re: Algebra and percentages - In need of helpful hints

11.7% ?!??!?! I had that calculation earlier when I was focusing on the distance speed time thing but thought it was too big for an increase! WTF!

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