Help on an easy speed/velocity problem?

Question

This is the last problem on my physics worksheet but I cannot for the life of me figure it out and it's really frustrating me. Can anyone explain to me how to do this?

"A speedy tortoise can run with a speed of 10.0 cm/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 2.0 minutes. The tortoise wins by a shell (20 cm).

a. How long does the race take?

b. What is the length of the race?

Answer 1

Distance(D) = rate(R) * time(t), t= tortoise, h = hare

Dt = Rt*t

Dt = 10t

Dh = Rt*20

Dt =Dh +20

10t = 20*Rt +20

10t = 20*10 + 20

t = 220/10 = 22 secs.

Dt = 10*22 =220 cm

Answer 2

Tortoise = 10 cm/s

Hare = 200 cm/s or 2 meters/s

The rabbit probably ran for 6.3 seconds before stopping.  

120 seconds = 12 meters for the tortoise.  

The race is probably 126.3 seconds long.  

Length of race = 60 centimeters + 1200 centimeters + 20 centimeters = 1280 centimeters or 12.8 meters

Answer 3

Hi Blackbird-

Race length = 12.6 meters

Time tortoise runs = 126 seconds

Time hare runs = 6.2 seconds      (all to 3 sig. figs)

======================================...

HOW TO DO IT:

The hare can rest anytime, so let's let him rest at the beginning.

The tortoise runs for t second while the hare runs for t-120 seconds

The hare covers D-.20 cm (the length of the race in cm) and the tortoise covers D during allof this.  D=rate * time

We have two equations in two unknowns...

D=10 * t

D-20 = 20*10 * (t-120)

Substituting...

t=D/10

D-20 = 200 (D/10 -120)

D-20 = 20D -24000 solving for D, we get a length of the race..

D = 1262 cm = 12.6 meters (3 sig. figs)

t=1263/10 = 126.3 sec

Check my #'s but the method is fine.

Now your worksheet is done!!  

-Fred