Old car radius=(Diameter of rim) / 2 + side wall height =13 /2 + 4.8=11.3 ( Sidewall height is calculated by Width of tire * side to height ratio. The treadwidth is taken to be 175mm instead of 170mm)
New car Radius =15/2 + 4.8(205/60)=12.3
Now we need to calculate the distance covered by both tires in one rotation. Since tyre is a circle that would be the circumference ( http://en.wikipedia.org/wiki/Circumference ) of both tires.
Circumference=2 * * Radius of tire
So,
For old tire C1=2 * (3.142) * 11.3=70.99 inches
For new tire C2=2 * (3.142) * 12.3=77.28 inches
Now to calculate the difference between them we can calculate their ratio
C2/C1=77.28/70.99 =1.088
This is the ratio by which the new tire travels more than old one. So, for equal rotation the difference between the distances travelled by both tires will be 1.088.
Therefore,
Since the old car travels 70km in 1 hour
New tire will travel=70*1.088 =76.16=76 km/h
Similarly,
Old car speed=100km/h ---] New car speed= 100*1.088=108.8 km/h ( Almost 109 km/h)
Old car speed=120km/h ----] New car speed=120 * 1.088=130.56 km/h ( Almost 130 km/h)
Hope this is right.
( VERIFIED from http://www.miata.net/garage/tirecalc.html. The ratio gives the same speed as the site.)