What a fantastically delightful little problem !
-- Both animals start at the sound of the starter's pistol, and the race is over
when the turtle crosses the finish line. The duration of the race is 'S' seconds.
-- The distance covered by any moving object is (speed) x (time) .
-- The turtle runs at 10 cm/s for 'S' seconds. He covers ' 10 S ' cm.
That's the length of the race.
-- The wabbit stops for 2 minutes = 120 seconds.
He runs for only (S - 120) seconds.
His speed is (10 x 20) = 200 cm/sec.
During the race, he covers ' 200 (S - 120) ' cm.
That's 20 cm less than the length of the race.
So the grand equation is 10 S = 200 (S - 120) + 20
Eliminate parentheses: 10 S = 200 S - 24,000 + 20
Combine like terms: 10 S = 200 S - 23,980
Subtract 10 S from each side: 0 = 190 S - 23,980
Add 23,980 to each side: 23,980 = 190 S
Divide each side by 190 : 126.21 = S (rounded)
The race lasted 126.21 seconds.
In that time, the turtle ran (10 x 126.21) = 1,262.1 cm <== the length
of the race
The rabbit ran for only (126.21 - 120) = 6.21 seconds
In that time, he ran (6.21 x 200) = 1,242 cm . . . 20 cm less than the turtle ran !
