Anna can ride a bicycle at 20 mph on pavement and 10 miles per hour on gravel. Anna is building a rectangular track with one side paved and three sides gravel. Anna would like to build the track so that it takes her 3 hours to ride all the way around the track. In this problem we find out how long the paved side should be if she wishes her track to enclose as large an area as possible.

Question

mathhelp346 · Answer

a. ( hint)Let the dimensions of the track be x and y where the paved side has
length x. Use Anna's speed on pavement and gravel to find an
equation in terms of x and y and find an expression in terms of x that
we wish to maximize

b. Determine how long the paves side should be if he wishes his track
to enclose as large an area as possible.