A problem of skiing really confusing

it was skiing resort in switzerland.i met a skiing enthusiast by the skiing slopes.he asked me to join him for lunch back in the spot where we were standing at 1pm after he had done a bit of skiing. i told him no,as i had an appointment to keep at 1pm.but if we could meet at 12 noon,i told him that perhaps i could manage.
then he said "i had calculated that if i could ski at 10km an hour i could arrive back at this spot by 1pm.that would be too late for you.But if i ski at the rate of 15km an hour,then i would reach back here at 11am.and that would be too early.now at what rate must i ski to get back here at 12 noon?"he got the right figure and he got back exactly at 12 noon.we had an excellent lunch.wat do you think the figure was? pls explain in details wit steps
note:the answer is not 12.5

assume the distance to be x that he covers
let the time taken be t hours from the time u met him first to 12 noon

at a speed of 10km he takes t+1 hrs to reach
10 = x/(t + 1)
similarly
15 = x/(t - 1)

equating the two

10t + 10 = 15t - 15
5t = 25
t = 5 hours

x = 60 km

and his figured speed, which gets him there at 12 noon
is x/t = 60/5 = 12 kmph

If the total distance she skis is x km, x/10 - x/15=2 since
there is a 2 hour difference in the two times. Solve to
give x=60 (which seems rather a long distance to be
skiing at a constant speed).
If she skis at y km/h then x/10-x/y=1 and x=60 gives
y=12 so 12 km/h seems to be the answer.