A tortoise runs at 12 cms and a hare can run 20 times faster In a race they both start at the same time but the hare stops for 4 min and the tortoise wins by 35 cm Find his time and length of the race?

Answer 1

Solution:

Tortoise travels at 12 so T_v*time = Distance

Hare travels at 240 so H_v*(time - 240 seconds) = Distance - 35cm or Distance = H_v*(time - 240 seconds)+35cm

Set them equal to each other and solve for "time". Then multiply time and the T_v to find the length of the race.

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The tortoise is traveling at 12 cm/sec and the hare at 240 cm/sec. When the tortoise has run for the time T in seconds, the values produce the equation

12 T = 240 (T-240) +35

Solving for T

240 T - 57600 + 35 = 12T

228 T = 57565

T = 252.478 seconds for the tortoise, traveling about 30.3 meters (3029.736 cm)

Tortoise 12 x 252.478 = 3029.736 cm

Hare 240 x 12.478 = 2994.720 cm (only runs 12.5 seconds, comes up short)

Tortoise wins by 35.016 cm