Just to let the people know, both my daughter and I had difficulty finding the solution to the given problem and answer because the book has typographical errors. Miles should be in kilometers and here's how my daughter got the solution:

Let X be the time covered for them to be 2 km apart.

IN DIAGRAM:
.............RATE......TIME......DISTANCE
Man 1..3km/hr.........X................3X........
Man 2..2km/hr.........X................2X........

EQUATION 1:
3X + 2X = 10 - 2
........5X = 8
... ......X = 8 / 5 or 1.6 or 1:36 HRS

EQUATION 2:
3X + 2X = 10 + 2
........5X = 12
..........X = 12 / 5 or 2.4 or 2:24 HRS

Thank you for those who tried to get the solution for us. I appreciate it...

There is no problem in the quiz, yes the student should conevrt miles to Km based on 1 mile = 1.6Km and accordingly solve the problem.
my solution for this problem will be as follows:
D1+D2+D3=16Km, where D1 is the distance the first travelr cross before reaching the enquired point, 3.2Km apart, D2 is the distance the second travler cross before reaching his point from his side, where D3 is 3.2Km. converting D=R*T and
based on the fact that at the specific point time will be equal the time will be required is 2.56hrs making the final results is 12+2.56 = 14h 33 mnt

We concluded that there was a problem with the question and it cost me 3000 chips to have the same solution I earlier explained to my daughter!

I am anxious to find out from daughter what has happened and she is still in school right now...

There's something I don't understand Laila. how the problem mixes km with miles??? Or are the students supposed to convert miles into kilometres?