Question

A turtle can run with a speed of 10.0 cm/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 2.00 mins. The turtle wins by 20.0 cm. how long does the race last? What is the length of the race?

Answer 1

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 !