how long does the race take?

Question

a tortoise can run with a speed of .1 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 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

speed turtle: 0.1m/s
speed of hare: .1 x 20 = 2m/s

2 min = 120s
20cm = .2m

They both start at the same time, but at a certain time the hare stops for 120s. Which is the same as the hare starts 120s after the turtle had started.

let t be the time of the turtle
t - 120 is the time of the hare

the turtle wins by .2m. That means the distance of the turtle goes minus the distance of the hare goes equals .2m

distance of the turtle: x = 0.1t
distance of the hare: x = 2(t-120)

0.1t - 2(t-120) = .2
0.1t - 2t + 240 = .2
-1.9t = -239.8
t = 126.2105263 s

b) the length of the race is the total distance the turtle goes
x = .1t
x = .1(126.2105263)
x = 12.62105263m

Answer 2

The length of race S = 10 t. where t is the time of race.

The hare has covered only (S- 20) cm in a time of (t- 120)s with a speed of 20 x 10 = 200 cm /s

S-20 / (t- 120) = 200

S-20 = 200(t- 120).

S = 10 t.

10 t. - 20 = 200(t- 120).

t = 126.21 s

S = 1262.1 cm

Answer 3

d/(0.1 m/s) = (d - 0.2)/(2 m/s) + 120 s
2d = 0.1(d - 0.2) + (2)(120)(0.1)
2d = 0.1d - 0.02 + 24
1.9d = 23.98
d = 12.621 m
t = 126.21 s