Question

I have a physics problem that the teacher says is an algebra problem:
"The tortoise and the hare were in a race. The tortoise went 10 cm/s and the hare went 200cm/s. The hare stopped at some point to take a 2 min nap, during which time the tortoise passed the hare, the hare woke up and started running but the tortoise won by 20 cm." I need to find the time for the race and the distance. How on Earth do I do that?

Answer 1

we could use simple equations:\[X_{tor}=V_{tor}t\]\[X_{hare}=V_{hare}t\]during the hare takes the nap it is stopped but the tortoise has been moving continuously.
so the position equation changes for hare:\[X_{hare}=V_{here}(t-120)\]at the end tortoise is 20cm further than hare, means:\[X_{tor}-X_{hare}=20cm (End)\]after substituting the above equations we could solve it for t, which is the race time. and again we substitute t in each of position equations to find the total distance traveled.

Answer 2

wait,so i need to put the distance at one end and solve it like an elimination problem?

Answer 3

first of all so sorry for my long absence...
you should put the motion equations of tortoise and hare in the last equation that expresses their positions at the last instant. then it could be solved easily for t.