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ΘTheta
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#1
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#1
Hi guys. I need help with 2 questions.
Q1. The ratio of seabirds to people on Gannet Island is 80:1. However, during the last twenty years the seabird population has fallen by 60 %, whilst the human population has increasedby 25%. What approximately was the ratio of seabirds to people on Gannet Island twenty years ago?

So 80*1.6=128 and 1/1.25=0.8. So 128:0.8 ===> 160:1, which is wrong.


Q2. A railway tunnel is 615 metres long. There is a strict speed limit of 45 kilometres per hour inside the tunnel and within 500 metres of either end.
The front of a train, whose length is 80 metres, has just entered the tunnel. The front of another train, of length 120 metres and travelling towards the tunnel in the opposite direction on a parallel track, is 40 metres away from the other end.
If both trains travel at the speed limit, how many seconds will it be before both trains have completely emerged from the tunnel? (Give your answer to the nearest second.)

I don't really know how to start this question:confused:

Thanks guys!
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Mr M
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(Original post by ΘTheta)
Hi guys. I need help with 2 questions.
Q1. The ratio of seabirds to people on Gannet Island is 80:1. However, during the last twenty years the seabird population has fallen by 60 %, whilst the human population has increasedby 25%. What approximately was the ratio of seabirds to people on Gannet Island twenty years ago?

So 80*1.6=128 and 1/1.25=0.8. So 128:0.8 ===> 160:1, which is wrong.


Q2. A railway tunnel is 615 metres long. There is a strict speed limit of 45 kilometres per hour inside the tunnel and within 500 metres of either end.
The front of a train, whose length is 80 metres, has just entered the tunnel. The front of another train, of length 120 metres and travelling towards the tunnel in the opposite direction on a parallel track, is 40 metres away from the other end.
If both trains travel at the speed limit, how many seconds will it be before both trains have completely emerged from the tunnel? (Give your answer to the nearest second.)

I don't really know how to start this question:confused:

Thanks guys!
Question 1:

You have the wrong multipler for a decrease of 60%.
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ΘTheta
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Report Thread starter 4 years ago
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(Original post by Mr M)
Question 1:

You have the wrong multipler for a decrease of 60%.
So you have to divide by 0.4 to represent an 60% increase?
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TenOfThem
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(Original post by ΘTheta)
So you have to divide by 0.4
Yes

to represent an 60% increase?
No
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RVNmax
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(Original post by ΘTheta)
So you have to divide by 0.4 to represent an 60% increase?
1) First of all a 60% increase is simply represented by a multiplication by 1.6, which is obviously what you initially tried.

I find it's very simple if you set up a simple equation. Let x = seabird population 20 yrs ago.

decreased by 60% means x - 0.6x = 80 (=0.4x)

so then x = 80/0.4,

so yes you are correct in that you need to divide by 0.4, but as previously mentioned, it doesn't represent a 60% increase, but rather removes a 60% decrease.



2) Well you can solve this question by working out how long it will take for each train to 'completely emerge' from the tunnel separately. You know the distances (be careful of which distances have been implied in the requirement) and you know the speed. Time is therefore quite simple to work out.
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