SOLUTION: Please help me. It's urgent. Question is "When Bob was as old as Rob was when Bob was half as old as Rob was when Bob was as old as Rob is, Rob was just a third as old as Bob w

  
You just had a period after the first phrase where you should 
have had a comma.


"When Bob was as old as Rob was when Bob was half as old
as Rob was when Bob was as old as Rob is, Rob was just a
third as old as Bob was when Rob was half as old as Bob
is. One is in their teens. What are their present ages?"

Suppose Bob is B years old and Rob is R years old.

Look at just the first phrase:

When Bob was as old as Rob was when Bob was half as old
as Rob was when Bob was as old as Rob is,

Let's translate these words on the end:

"when Bob was as old as Rob is,"

to a number of years ago.  Bob is older than Rob, so we
subtract their ages, B-R to find out how many years ago
that was.  So we rewrite the phrase as:

"When Bob was as old as Rob was when Bob was half as old
as Rob was B-R years ago."

Let's translate these words on the end:

"as old as Rob was B-R years ago."

to an age.  To find that, we subtract B-R years from
Rob's age now, which is R and get

R-(B-R)
R-B+R
2R-B

So now we have

"When Bob was as old as Rob was when Bob was half of 2R-B"

Let's translate the words on the end:

"half of 2R-B"

to an age as 


 years old

So now we have

"When Bob was as old as Rob was when Bob was 
years old."

Let's translate the words on the end:

"when Bob was  years old"

to a number of years ago.  To find how many years ago
that was, we subtract " from Bob's age now, 
which is B:



 years ago.

So now we have

"When Bob was as old as Rob was  years ago.

Let's translate the words on the end:

"as old as Rob was  years ago."

We subtract that from Rob's age now:





So now we have

"When Bob was  years old."

We translate that to a number of years ago by subtracting
it from B:



 years ago.

Now we look at the second phrase:

"Rob was just a third as old as Bob was when Rob was half
as old as Bob is"

Notice the first two words:

"Rob was".

Let's replace that by Rob's age  years ago.  We do that by subtracting it from Rob's age now,
which is R:





and put an = sign after it because that is the subject of
the second phrase:

" just a third as old as Bob was when 
Rob was half as old as Bob is"

Let's translate the words on the end:

"half as old as Bob is"

That's simply  years old.

So now we have:

" just a third as old as Bob was when Rob 
was  years old."

Let's translate the words on the end:

"when Rob was  years old."

to a number of years ago.  We do that by subtracting  
years from Rob's age now, which is R:

 years ago.

So now we have:

" just a third as old as Bob was 
 years ago."

Let's translate the words on the end:

"as old as Bob was  years ago"

to the age of Bob then.  We do that by subtracting  
from Bob's age now, which is B:




 
So now we have:

 just a third (of) 

So we just put  in front of that:



Multiply both sides by 6







That simplifies to





So R must be divisible by 9,

 So R =  9, 18, 27, 36, 45, 54, 63, 72, 81, 90,...

And B = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,... 

Now we use this sentence:

"One is in their teens."

There is only one possibility,

Rob is 18 and Bob is 20.

Edwin