this question can be attempted in many ways... first the algebra method.
Let the number of hours the motorist drives be x
Let his speed be y

Now in normal course he travels xy miles

(x+1)(y+5)=xy+70

=> 5x+y+5 = 70
5x +y = 65

Now if he travels 2 hours longer and 10 miles faster

The distance travelled = (x+2)(y+10)

= xy + 10x+2y+20 = xy+130+20 (substituting the value of 5x+y = 65 in 2(5x+y)+20
=xy+150

Hence he travels 150 miles extra

------------------------------------------
the other approach can be

He covered 70 miles more in an hour by driving 5 miles/hour faster.

Hence his speed current is 70 mile/hr
his original speed will be 65 miles/hr......WHY?? because he is traveling 5mile/hr faster).
Therefore his new speed will be 75miles/hr (given 10 mile/hr faster)
hence distance traveled will be 75*2 = 150


Hope it helps....

Awsome. Thank you for the detailed explanation.

Cheers,