Question 1137736
<pre>
d=rt
Using units of hours for time, km for distance:

r=d/t = 200/t     (1)

We are given:
r+2 = d/(t-1/4)  (2)     

Solving each for t and then setting them equal to eliminate t:
{{{ 200/r =  200/(r+2) - (1/4) }}}

Re-arranging and then simplifying:
{{{  r^2 + 2r - 1600 = 0 }}}

Solving:
{{{ r = -1 +- sqrt(1601) }}} 

Taking positive result:    {{{ highlight(r = 39.012) }}} km/hr

-----------
Check:  Add 2km/hr to the above:  41.012 km/hr

At 39.012km/hr the trip takes  200km/(39.012km/hr) = 5.1266hr
At 41.012km/hr the trip would take 200km/(41.012km/hr) = 4.8766hr

The difference is  0.25hr which is 15 minutes.