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Question

Otto and Kurt are going snowboarding. Otto sets off down a 2000 m run. Kurt starts 30 seconds after Otto (taking longer to strap on his board, and untuck his shirt to look cool.) He decides to go down an easier, shorter, 1680 m run and goes 4 m/s faster than Otto. How fast was Otto going if both arrive at the bottom of the hill at the same time?

Answer 1

1st equation:

2000 = r(t+30)  = rt + 30r

 

2000 - 30r = rt

 

2nd equation:

1680 = (r+4)t = rt + 4t

 

 

1680 = 2000 - 30r + 4t

 

-320 = -30r + 4t

 

-160 = -15r + 2t

 

15r - 160 = 2t

 

(15r-160)/2 = t

 

 

2000 = r ( 15r - 160)/2

 

4000 = 15r^2 - 160r

 

0 = 15r^2 - 160r - 4000

 

0 = 3r^2 - 32r - 800

 

r=22.5412

 

 

  2000 = 22.5412* (t+30) ---> t = 58.72