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 2.0 minutes. The tortoise wins by a shell (20 cm)!How long does the race take?What is the length of the race?

a. 126.21secs

b. 12.621 meters.

Explanation:

Given data:

Speed of tortoise = 0.1m/s.

Speed of hare = 2m/s.

Solution:

a. Distance traveled = Speed* Time

Speed of tortoise = 0.1 m/s

Speed of hare = 20*0.1 m/s = 2 m/s

2 minutes = 2* 60 s = 120 s

Let the time taken for the race be t seconds.

• Distance moved by tortoise

= (0.1 /s)* (t s)

= 0.1*t meter

•Hare has run for a time of (t - 120)s.

distance moved by hare

= Speed * Time

= (2 m/s)*(t- 120)s

= (2t - 240) meter.

Since hare is 20 cm (0.2 m) behind the tortoise, therefore

(0.1*t - 0.2) meter

= (2t - 240) meter

0.1*t - 0.2 = 2t - 240

Collect like terms

239.8 = 1.9t

Divide both sides by 1.9

t = 126.21secs

The race lasted for 126.21secs

b. Length of race

= Distance moved by tortoise

= 0.1*126.21 meter

= 12.621 meter

The length of the race is 12.621 meters.