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
Oct 17, 2015

The question as given has no positive solutions.

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

Explanation:

The question as given has no positive solutions.

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

We are given:

x = 4y

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

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

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

Subtract 40 from both sides to get:

y = -32

Then

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

So Petra is -128 and Philippa is -32

Alternative problem

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

Then we are given:

x = 5y

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

Subtract the second equation from the first to get:

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

Add 32 to both ends to get:

y = -8 + 32 = 24

Then

x = 5y = 5*24 = 120

So Petra is 120 and Philippa is 24

Oct 17, 2015

Petra = -32, Philippa = 94
Given that initial condition year is t_0, Petra had not been born. She would be in 32 years that is, 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
Let time in 8 years be t_8
Let Petra be "Pe"
Let Philippa be "Ph"

At t_o -> "Pe" = 4"Ph"
Then "Pe - 4"Ph" = 0.................. ( 1 )

At t_8 -> "Pe" + 8 = 5("Ph" + 8)
Then "Pe" -5"Ph" = 40 - 8 = 32....... ( 2 )

Subtract ( 1 ) from ( 2 ) giving:

-"Ph" = 32
So "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
If at t_0 " Pe" is four times older then, stepwise we have from "Ph's" age:

(-32), 32, 32, 32

So "Pe's" age at t_0 is 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