Solve a Race Problem: Tortoise and Hare Finish Time and Length

[princesspriya]

in a race, a tortoise runs at 10cm/s and hare runs at 200cm/s. both start at the same time, but the hare stops to rest for 2.00 min. The tortoise wins by 20.0cm.
Part 1) At what time does the tortoise finish the line?

Part 2) What is the length of the race?

I would really appreciate it if you guys could show me how you got the answer
thank you
-its not a homework question. i found this question online and i just wanted to make sure i no how to do it for my test

 

[nawab pasha]

I don't how to type equations here. let me try.
x-total distance
x-20cm is the distance traveled by hare while tottoise completes x distance.
t-time taken by tortoise to complete x distance
the excess time spent by hare=120 seconds(2minutes)
v-velocity of tortoise
v'-velocity of hare
then,
t=x/v=((x-20)/v')-120

i think u can solve this x and then find t. if u find any difficulty u are always welcome.

 

[Moetasim]

Part 1) To find the time it takes for the tortoise to finish the race, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. We know that the tortoise runs at a rate of 10cm/s and the hare runs at a rate of 200cm/s. Let's assume that the race is over when the tortoise reaches the finish line. Since the tortoise wins by 20.0cm, we can set up the equation 10t = 200t - 20. Solving for t, we get t = 1/19 minutes, or approximately 3.16 seconds. This means that the tortoise finishes the race in 3.16 seconds.

Part 2) To find the length of the race, we can use the same equation d = rt, but this time we are solving for d. We know that the tortoise runs for 3.16 seconds and the hare runs for 2 minutes, or 120 seconds. The distance traveled by the tortoise is 10cm/s x 3.16s = 31.6cm. The distance traveled by the hare is 200cm/s x 120s = 24000cm. Since the tortoise wins by 20.0cm, we can subtract 20.0cm from the hare's distance to find the total length of the race. Therefore, the length of the race is 24000cm - 20.0cm = 23980cm.

I hope this helps! Let me know if you have any further questions or if you need clarification on any of the steps. Remember to always check your units and make sure they are consistent throughout the problem. Good luck on your test!