How Do You Solve the Tortoise & Hare Race Problem?

In summary, the problem involves a tortoise and hare racing, with the hare running 20 times faster than the tortoise. The hare stops to rest for 5.0 minutes, but the tortoise still wins by a shell (40 cm). The equations used are dt = 0.10t and dh = (20)(0.10)(t-300), and by setting them equal to each other, the time and length of the race can be solved for.
  • #1
aznbaby
1
0

Homework Statement


A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 5.0 minutes. The tortoise wins by a shell (40 cm).
(a) How long does the race take? (s)
(b) What is the length of the race? (m)

Homework Equations



d= distance
s= speed
t= time
subscripts;
h=hare
t=tortoise

dh=sh x th
dt=st x tt


The Attempt at a Solution



i have these two equations:

dt-0.40=(20)(0.10)(t-300)

d=0.10t

how do i set them equal to each other
or how do i solve them? i have no clue...
 
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  • #2
Welcome to PF!

Hi aznbaby! Welcome to PF! :smile:
aznbaby said:
i have these two equations:

dt-0.40=(20)(0.10)(t-300)

d=0.10t

how do i set them equal to each other
or how do i solve them? i have no clue...

(shouldn't the second equation also be dt?)

Just put the two d's equal :wink: …

which gives you t = … ? :smile:​

(though personally I'd have defined dh = (20)(0.10)(t-300), and then put dh = dt - 0.40)
 

FAQ: How Do You Solve the Tortoise & Hare Race Problem?

1. What is the main difference between the motion of the tortoise and the hare?

The main difference is the speed at which they move. The hare moves at a much faster pace while the tortoise moves at a slower, more consistent pace.

2. How does the distance covered by the tortoise and the hare change over time?

The distance covered by the tortoise and hare changes as the time increases. The hare will cover a larger distance compared to the tortoise due to its faster speed.

3. What factors affect the motion of the tortoise and the hare?

The motion of the tortoise and hare can be affected by factors such as the terrain, the physical abilities of the animals, and external factors like weather conditions.

4. Can the tortoise ever catch up to the hare in a race?

In theory, yes, the tortoise can catch up to the hare in a race. This can occur if the hare stops or slows down significantly, allowing the tortoise to make up for lost time.

5. How does the concept of acceleration apply to the motion of the tortoise and the hare?

Acceleration refers to the change in speed or direction of an object over time. In the case of the tortoise and hare, the hare's faster speed can be seen as a form of acceleration compared to the steadier pace of the tortoise.

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