Problem: A and B move uniformly along two straight paths intersecting at right angles in point O. When A is at O,B is 500 yards short of O. In 2 minutes they are equidistant from O, and in 8 minutes more they are again equidistant from O. Then the ratio of A's speed to B's speed is:
Answer Choices:
A. 4:5
B. 5:6
C. 2:3
D. 5:8
E. 1:2
Solution:
Let rA represent the speed of A, and let rB represent the speed of B.
rBx=2,rA500−x=2,x=2rB
∴rA500−2rB=2,rA+rB
=250
rB500−x+y=8,rAy−500+x=8
y−500+x=8rAy+500−x=8rB}2y=8(rA+rB)=8⋅250y=1000
8rB=1000+500−2rB,rB=150∴rA=100∴rA:rB=2:3
