Question #c5e8c

We're asked to find the minimum distance from the goal that the tortoise can be so that the hare and tortoise reach the finish line at essentially the same time.

We're given that the tortoise's speed is constant at #0.200# #"m/s"#, and that the speed of the hare is #8.00# #"m/s"#.

The hare stops at a distance #0.800# #"km"#, i.e. #200# #"m"# from the finish line. We'll call this the position #x = 0#.

What we're essentially trying to find is the distance from the finish line (i.e. position #x = 200# #"m"#) the tortoise must be so that they meet at position #x = 200# #"m"# at the same time.

The time it would take the hare to travel #200# #"m"# is

#"time" = "distance"/"speed" = (200cancel("m"))/(8.00cancel("m")"/s") = color(red)(ul(25color(white)(l)"s"#

Now what we do is calculate the distance the tortoise can travel at its maximum speed during this time, and this will be the distance from the finish line we're asked to find:

#color(blue)("distance") = ("speed")("time") = (0.200color(white)(l)"m/"cancel("s"))(color(red)(25)cancel(color(red)("s"))) = color(blue)(ulbar(|stackrel(" ")(" "5color(white)(l)"m"" ")|)#