Question 785534
{{{t}}} = hours takem for the round trip
{{{r}}} = hours taken for the return trip
{{{t=r+(r-2)}}}-->{{{t=2r-2}}}-->{{{t+2=2r}}}-->{{{r=(t+2)/2}}}
{{{d}}} = distance to the station = distance traveled back from the station
For the round trip we know that
{{{50t=2d}}}
For the return trip we know that
{{{d=30((t+2)/2)}}}-->{{{d=30(t+2)/2}}}-->{{{d=15(t+2)}}}-->{{{d=15t+30}}}
Substtituting that expression for {{{d}}} into {{{50t=2d}}} we get
{{{50t=2*(15t+30)}}}-->{{{50t=30t+60}}}-->{{{50t-30t=60}}}-->{{{20t=60}}}-->{{{highlight(t=3)}}}
Unfortunately, what that means for the trip distances and speeds is scary:
{{{2d=50*3}}}-->{{{2d=150}}}-->{{{d=150/2=75}}}
{{{r=(3+2)/2}}}-->{{{r=2.5}}}
If the trip back took 2.5 hours and the trip to the station took 2hours less,
{{{2.5h-2h=0.5h}}},
Mary drove the 75 miles to the station in 0.5 hours.
Her average speed when going to the station was
{{{75miles/("0.5 hours")=150mph}}}