A tortoise can run with a speed of 0.1 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

Question

2.0 mins. The tortoise wins by a shell (20cm). 

(A) How long does the race take?

(B) what is the length of the race? 

Answer 1

distance = rate x time

 

             = 0.1 m/s x time <---- tortoise

 

            

(distance - 20 cm) = (20 x 0.1 m/s) x (time - 2 min)  <--- hare

 

 

Measurements have to be the same ( meters , seconds).....

 

tortoise:  distance = 0.1 m/s * time

 

hare :     (distance - 0.2 m) = ( 2 m/s) * (time - 120 sec)

 

Now, changes them to variables, distance = d, time = t:

 

                 d = 0.1 m/s * t

 

              (d - 0.2 m) = (2 m/s) * (t - 120 sec)

 

           0.1 m/s * t - 0.2 m  =  (2 m/s)*(t - 120 sec)

 

            0.1 m/s * t - 0.2 m = 2 m/s * t - 240 m  <--- distributive right side; seconds cancel

 

            1 m/s * t - 2 m = 20 m/s * t - 2400 m <--- multiplies everything by 10 to clear the decimals

 

            0 = 20 m/s * t - 2400 m - 1 m/s * t + 2m <---- moves everything to right side,changes signs

 

           0 = 19 m/s * t - 2398 m

 

           2398 m = 19 m/s * t  <--- solves for t

 

            2398 m / 19 m/s = t

 

            t = 2398/19 sec  = 126.21053 sec

 

               = 2 minutes ant 6.21 sec

 

        

   The length is the race, traveled by the tortoise who completed it, is

 

    distance = (0.1 m/s) * 126.21053 sec = 12.621053 meters

 

   

The rabbit went 126.21053 sec - 120 seconds = 6.21053 seconds because it stopped for 2 minutes.

6.21053 seconds x 2 m/s = 12.42106 meters.

12.621053  12.42106 = 0.2 which is the length of the tortoise shell.

So the answers are proven correct.

 

The race took  t = 2398/19 sec = 126.21053 sec = 2 minutes ant 6.21 sec

and the length of the race course is 12.621053 meters