# Speed of Racer

Question: In a Road Race, one of the three bikers was doing 15km less than the first and 3km more than the third. He also finished the race 12 minutes

after the first and 3 minutes before the third. Can you find out the speed of each biker, the time taken by each biker to finish the race and the length of the course? Assume that there were no stops in the race and also they were driving with constant speedsthrough out the race.

Let us assume that
Speed of First biker = V1 km/min
Speed of Second biker = V2 km/min
Speed of Third biker = V3 km/min
Total time take by first biker = T1 min
Total distance = S km
Now as per the data given in the teaser, at a time T min
X1 = V1 * T ----> 1
X1 - 15 = V2 * T ----> 2
X1 - 18 = V3 * T ----> 3
At a Distance S Km.
S = V1 * T1 ----> 4
S = V2 * (T1 + 12) ----> 5
S = V3 * (T1 + 15) ----> 6
Thus there are 6 equations and 7 unknown data that means it has infinite number of
solutions.
By solving above 6 equations we get,
Time taken by first biker, T1 = 60 Min.
Time taken by Second biker, T2 = 72 Min.
Time taken by first biker, T3 = 75 Min.
Also, we get
Speed of first biker, V1 = 90/T km/min
Speed of second biker, V2 = (5/6)V1 = 75/T km/min
Speed of third biker, V3 = (4/5)V1 = 72/T km/min
Also, the length of the course, S = 5400/T km
Thus, for the data given, only the time taken by each biker can be found i.e. 60, 72 and 75
minutes. For other quantities, one more independent datum is required i.e. either T or V1
or V2 or V3