Let Jorge's speed be j mph and Rosa's be r mph.
Jorge takes 162/j hours to drive 162 miles. Rosa takes 135/r hours to drive 135 miles.
We are given that Jorge takes two hours less. So if we add 2 to Jorge's hours we get Rosa's.
162/j + 2 = 135 / r. We get (162 + 2 j ) / j = 135 / r
But we are also given that Jorge drives two times faster than Rosa. So, j = 2r.
Substituting in the above expression we get (162 + 4r) / 2r = 135 / r. Cancel the r from the denominator on both sides. On the left, divide by 2. Then 81 + 2r = 135. Therefore 2r = 54, that is, r = 27 and, of course, j = 2 x 27 = 54.
Back check, please. I have. It is corrrrrrrect!
Dattaprabhakar (Dr, G,)
This is 2 hours less than Rosa takes (to drive 135 miles).
So Rosa takes (162/j) + 2 hours to drive 135 miles.
We are given that Jorge was two times faster than Rosa. So Jorge's speed must be 2R. (we need not use J any more)
Jorge takes 162 / (2R) hours to drive 162 miles. 162/(2R) = 81 / R.
This is two hours less that it takes Rosa.
So Rosa takes (81 / R) + 2 = (81+2R)/ R hours to drive 135 miles.
Rosa's speed is 135 / [(81 + 2R) / R] = (135 R) / (81 + 2R)