math riddle. head start of 10 miles, guard is walking 1 mph faster, how long until they catch up?
a prison guard and his blood hound are chasing an escaped prisoner. the prisoner has a 10 mile head start but the guard is walking 1mph faster than the prisoner. The bloodhound is trained to run to the prisoner, then run back to the guard, then continue running back and forth between them. If the bloodhound runs 10 mph, how far does the bloodhound run before the guard finally catches up to the prisoner?
Well every hour for ten hours they lose 1 mile of distance. The first hour the bloodhound goes to the prisoner, the second hour he comes back and has a mile left to spare. The third hour the bloodhound has excess of 2 miles plus 1, and the fourth hour excess of 3 + 3 + 1 until the 10th hour when the bloodhound has excess of 1 + 3 + 3 + 5 + 5 + 7 + 7 + 9 + 9 plus 10*10 so that totals 149 miles in 10 hours.
–Edit–
I realized something. This is impossible to calculate if the dog is running 10mph. However, if the dog is running 10mph faster than the prisoner (so that the prisoner is your frame of reference) what I put above should be correct, as far as I know.
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