1968 AMC 12 Problem 32

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

Let the speeds be

u,

v

; at

t=2,

2u=500-2v

At

t=10,

B

has passed

O,

so

10u=10v-500

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.

Problem 32 in other years