Petra is 4 times as old as Philippa. In 8 years time she will be 5 times as old as Philippa. How old are Philippa and Petra?

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Petra is 4 times as old as Philippa. In 8 years time she will be 5 times as old as Philippa. How old are Philippa and Petra?

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Answer 1 · 2015-10-17T08:37:49

The question as given has no positive solutions.

If the $4$ $4$ and $5$ $5$ were the other way round then Petra's current age is $120$ $120$ and Philippa's $24$ $24$ .

Explanation:

The question as given has no positive solutions.

Let Petra's current age be $x$ $x$ and Philippa's $y$ $y$ .

We are given:

$x = 4 y$ $x = 4y$

$x + 8 = 5 (y + 8) = 5 y + 40$ $x+8 = 5(y + 8) = 5y + 40$

Subtract the first of these equations from the second to get:

$8 = x + 8 - x = 5 y + 40 - 4 y = y + 40$ $8 = x+8 - x = 5y+40 - 4y = y + 40$

Subtract $40$ $40$ from both sides to get:

$y = - 32$ $y = -32$

Then

$x = 4 y = 4 (- 32) = - 128$ $x = 4y = 4(-32) = -128$

So Petra is $- 128$ $-128$ and Philippa is $- 32$ $-32$

Alternative problem

Suppose the $4$ $4$ times and $5$ $5$ times were supposed to be the other way round.

Then we are given:

$x = 5 y$ $x = 5y$

$x + 8 = 4 (y + 8) = 4 y + 32$ $x + 8 = 4(y+8) = 4y + 32$

Subtract the second equation from the first to get:

$- 8 = x - (x + 8) = 5 y - (4 y + 32) = y - 32$ $-8 = x - (x + 8) = 5y - (4y + 32) = y - 32$

Add $32$ $32$ to both ends to get:

$y = - 8 + 32 = 24$ $y = -8 + 32 = 24$

Then

$x = 5 y = 5 \cdot 24 = 120$ $x = 5y = 5*24 = 120$

So Petra is $120$ $120$ and Philippa is $24$ $24$

Answer 2 · 2015-10-17T09:17:28

Petra = -32, Philippa = 94
Given that initial condition year is $t_{0}$ $t_0$ , Petra had not been born. She would be in 32 years that is, $t_{32}$ $t_32$ . Consequently Petra's age is negative.

Explanation:

I gave the wrong answer originally. Submission deleted!
Hopefully I will not get interrupted this time!!! Wrong, 4th attempt!

Let current time be $t_{0}$ $t_0$
Let time in 8 years be $t_{8}$ $t_8$
Let Petra be $Pe$ $"Pe"$
Let Philippa be $Ph$ $"Ph"$

At $t_{o} \to Pe = 4 Ph$ $t_o -> "Pe" = 4"Ph"$
Then $Pe - 4 P h = 0$ $"Pe - 4"Ph" = 0$ .................. ( 1 )

At $t_{8} \to Pe + 8 = 5 (Ph + 8)$ $t_8 -> "Pe" + 8 = 5("Ph" + 8)$
Then $Pe - 5 Ph = 40 - 8 = 32$ $"Pe" -5"Ph" = 40 - 8 = 32$ ....... ( 2 )

Subtract ( 1 ) from ( 2 ) giving:

$- Ph = 32$ $-"Ph" = 32$
So $Ph = - 32$ $"Ph" = -32$ .................... ( 3 )

( at first this looks as though it is not possible. However if you view negative age as to be born in the future then it works. So -32 means that $Ph is to born at t_{32}$ $"Ph is to born at " t_32$
If at $t_{0} Pe$ $t_0 " Pe"$ is four times older then, stepwise we have from $Ph's$ $"Ph's"$ age:

(-32), 32, 32, 32

So $Pe's$ $"Pe's"$ age at $t_{0}$ $t_0$ is $32 + 32 + 32 = 94$ $32 + 32 + 32= 94$ because $Ph's$ age is 32 years the other side of 0 giving a total of $4 times 32 = 128$ years difference. ( $94 - (-32)) = 128$

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Petra is 4 times as old as Philippa. In 8 years time she will be 5 times as old as Philippa. How old are Philippa and Petra?

2 Answers

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