Question

$A$ 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:

$4:5$

$5:6$

$2:3$

$5:8$

$1:2$

Answer: C

Concepts:distance rate and time system of equations

Difficulty rating: 1900

Small Hint:

Let the speeds be $u,$ $v$ ; at $t=2,$ $2u=500-2v$

Big Hint:

At $t=10,$ $B$ has passed $O,$ so $10u=10v-500$

Solution:

Let the speeds of $A,$ $B$ be $u,$ $v.$ At $t=2,$ $2u=500-2v,$ so $u+v=250.$ At $t=10,$ $B$ has passed $O,$ and $10u=10v-500,$ so $v-u=50.$ Hence $u=100,$ $v=150,$ and $u:v=2:3.$

Therefore, the correct answer is C.

1968 AMC 12 Problem 32

Answer: C

Difficulty rating: 1900

Small Hint:

Big Hint:

Solution:

Problem 32 in Other Years