Problem: In racing over a given distance d, at uniform speed, A can beat B by 20 yards, B can beat C by 10 yards, and A can beat C by 28 yards. Then d, in yards, equals:
Answer Choices:
A. Not determined by the given information
B. 58
C. 100
D. 116
E. 120
Solution:
Let vA,vB,vC be the respective speeds of A,B,C.
∴ (1) vAd=vBd−20 (2) vBd=vCd−10
(3) vAd=vCd−28∴(4)vBd−20=vCd−28. Divide equation (4) by equation (2) and obtain dd−20=d−10d−28∴d=100