Abicyclist pedals along a straight road with velocity, v, given in the figure below. she starts 7 miles from a lake; positive velocities take her away from the lake and negative velocities take her toward the lake.

when is the cyclist farthest from the lake?

approximately how far away is she at this time? give a best estimate. (round your answer to the nearest whole number.)

The separation went from the beginning stage is given by the range under the speed chart.
The territory under the x-hub is figured as negative zone, and positive over the x pivot.
 For this situation,
 we should do estimate for the region under the chart. I like thinking regarding boxes initially, and I'd say the initial 20 minutes, we have around 1 full negative box,
then 7 full positive boxes from 20 mins to 60 minutes.
Boxes=7-1
=6.
 So remove from lake at t=1 hour is
7miles+6boxes*areaOfABox;
where
 areaOfABox=10*1/6
=1.77

What sports are they giving you