In racing over a given distance, A can beat B by 20m, B can beat C by 10m, A can beat C by 28m. The racing distance is?
a) 58 m
b) 116 m
c) 100 m
d) 120 m
e) cannot be determined
Let the uniform speeds of A,B,C be vA,vB,vC, respectively.
Let t1 be the time taken for the race between A and B and t2 be the time taken for race
between B and C
Since A covers the distance in time t1, race between A and C also takes time
t1.Therefore,
VAt1-VBt1 =20
VBt2 –Vct2=10
VAt1 - Vct1=28
Also, VAt1=VBt2 = d. Thus VBt1 =d-20, Vct2=d – 10 and VCt2= d – 10 and VCt1=d-28.
(d-20)/(d-28) = VB/ VC = d/(d-10)
Thus (d-20)(d-10)=d(d-28).Hence, d=100.
Answer: c)