Question 62053
Let the speed of Smith be x mph

Then speed of Jones = (x+5) mph

Distance covered by Smith = 45 miles.

So time taken by Smith = Distance/time
                       = 45/x hrs

Distance covered by Jones = 70 miles.
Time taken by Jones = 70/(x+5) hrs.

By the given data,

70/(x+5) - 45/x = 1/2

Multiplying throughout by 2x(x+5) we get,
70*2x - 45*2(x+5) = x(x+5)

==> 140x - 90x - 450 = x^2 + 5x
==>50x - 450 - x^2 - 5x = 0
==> -x^2 + 45x - 450 = 0
==> x^2 - 45x + 450 = 0

==> x^2 - 15x - 30x + 450 = 0
==> x(x-15) - 30(x - 15) = 0
==> (x-15)(x-30) = 0
==> x-15 = 0   or  x-30 = 0
==> x = 15 or x = 30

So either their speeds are 15 mph  and 20 mph  Or
 their speeds are 30 mph  and 35 mph respectively.
In either cases the difference in time taken = 1/2 hr.


Good Luck!!!