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.
rB​x​=2,rA​500−x​=2,x=2rB​
∴rA​500−2rB​​=2,rA​+rB​
=250
rB​500−x+y​=8,rA​y−500+x​=8
​y−500+x=8rA​y+500−x=8rB​​}​2y=8(rA​+rB​)=8⋅250y=1000​​
8rB​=1000+500−2rB​,rB​=150∴rA​=100∴rA​:rB​=2:3
