# Maths problem solving question

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Question: Winnie lives in a village in rural Africa which is marked as (2,3) on a map.

Each day she goes to a river which flows due East, she fills a bucket with water at R and takes it to her grandmother who lives in the nearby Village Q. Winnie wants to know where to fill the buckets so that she has the shortest distance to walk.

P is (2,3), Q is (8,1), the equation of the river is y=5, please may you tell me why the shortest route from P to the river and then to Q is P -> (4,5) -> Q? 😄

Each day she goes to a river which flows due East, she fills a bucket with water at R and takes it to her grandmother who lives in the nearby Village Q. Winnie wants to know where to fill the buckets so that she has the shortest distance to walk.

P is (2,3), Q is (8,1), the equation of the river is y=5, please may you tell me why the shortest route from P to the river and then to Q is P -> (4,5) -> Q? 😄

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#2

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Question: Winnie lives in a village in rural Africa which is marked as (2,3) on a map.

Each day she goes to a river which flows due East, she fills a bucket with water at R and takes it to her grandmother who lives in the nearby Village Q. Winnie wants to know where to fill the buckets so that she has the shortest distance to walk.

P is (2,3), Q is (8,1), the equation of the river is y=5, please may you tell me why the shortest route from P to the river and then to Q is P -> (4,5) -> Q? 😄

**Freedom physics**)Question: Winnie lives in a village in rural Africa which is marked as (2,3) on a map.

Each day she goes to a river which flows due East, she fills a bucket with water at R and takes it to her grandmother who lives in the nearby Village Q. Winnie wants to know where to fill the buckets so that she has the shortest distance to walk.

P is (2,3), Q is (8,1), the equation of the river is y=5, please may you tell me why the shortest route from P to the river and then to Q is P -> (4,5) -> Q? 😄

Then the total distance to walk is

Now you want to minimise . This means setting . This then yields that .

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#3

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...

**Freedom physics**)...

From P, she has to go up to R.

If you reflect P in the line y=5, to P' say, you have effectively the same problem. P and P' are as far from the river as each other, and the distance to any point on the river is the same for each.

The problem now becomes what's the shortest distance from P' to Q, and it will automatically go via the river.

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#4

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RDKGames has given you one method, though there is no need to get into calculus to solve this.

From P, she has to go up to R.

If you reflect P in the line y=5, to P' say, you have effectively the same problem. P and P' are as far from the river as each other, and the distance to any point on the river is the same for each.

The problem now becomes what's the shortest distance from P' to Q, and it will automatically go via the river.

**ghostwalker**)RDKGames has given you one method, though there is no need to get into calculus to solve this.

From P, she has to go up to R.

If you reflect P in the line y=5, to P' say, you have effectively the same problem. P and P' are as far from the river as each other, and the distance to any point on the river is the same for each.

The problem now becomes what's the shortest distance from P' to Q, and it will automatically go via the river.

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#5

(Original post by

That's neat!

**RDKGames**)That's neat!

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The book used the same method although it reflected Q instead, although I found the equation of the line connecting P' to Q and when you sub in y=5 into it it gives R as (5,5), please may you help me with this? 🙂

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Tbh I think the book's miscalculated something because I've just done it their wae and for exactly the same result!

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The book used the same method although it reflected Q instead, although I found the equation of the line connecting P' to Q and when you sub in y=5 into it it gives R as (5,5), please may you help me with this? 🙂

**Freedom physics**)The book used the same method although it reflected Q instead, although I found the equation of the line connecting P' to Q and when you sub in y=5 into it it gives R as (5,5), please may you help me with this? 🙂

Post your working. You should have P' is the point (2,7).

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Why would P' be (2,7), I thought it was (2,8) because P is three units away from y=5 so P'should be three units above it 🙂

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#11

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Why would P' be (2,7), I thought it was (2,8) because P is three units away from y=5 so P'should be three units above it 🙂

**Freedom physics**)Why would P' be (2,7), I thought it was (2,8) because P is three units away from y=5 so P'should be three units above it 🙂

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Thanks for pointing that out! And when I said them I referred to the coordinates of P! 😄

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Yeah, I'm not sure how that reply came out as that because I posted something completely different and never even typed a ... 😂

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#16

**Freedom physics**)

Why would P' be (2,7), I thought it was (2,8) because P is three units away from y=5 so P'should be three units above it 🙂

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