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) vA​d​=vB​d−20​ (2) vB​d​=vC​d−10​
(3) vA​d​=vC​d−28​∴(4)vB​d−20​=vC​d−28​. Divide equation (4) by equation (2) and obtain dd−20​=d−10d−28​∴d=100