A tortoise can run at 10 cm s- and a hare can run 30 times as fast. In a race, they start at the same time, but hare stops and takes rest for 3 minutes and so the tortoise wins by 30 cm. (a) How long does the race take place? b) What is the length of the race?
Answers
Given : A tortoise can run at 10 cm/s-
A hare can run 30 times as fast.
In a race, they start at the same time,
but hare stops and takes rest for 3 minutes and so the tortoise wins by 30 cm.
To Find : (a) How long does the race take place?
b) What is the length of the race?
Solution:
Speed of Tortoise = 10 cm/s
Hare Speed = 30 x 10 = 300 cm/s
hare stops and takes rest for 3 minutes
Time of Travel by hare = t secs
Time of travel by Tortoise = t + (3 * 6) = t + 180 secs
Distance travelled by tortoise = 30 cm more
Distance = Speed x time
Hence
10 ( t + 180) = 300 * t + 30
=> t + 180 = 30t + 3
=> 29t = 177
=> t = 177/29
=> t ≈ 6.1 secs
Race time = 180 + 6.1 = 186.1 secs
Length of Race = 10 ( 177/29 + 180) ≈ 61.03 + 1800
≈ 1861.03 cm
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Answer:
time:186.08secs
distance:1860.8cm
