1953 AMC 12 Problem 41

Question

A girls’ camp is located

300

rods from a straight road. On this road, a boys’ camp is located

500

rods from the girls’ camp. It is desired to build a canteen on the road which shall be exactly the same distance from each camp. The distance of the canteen from each of the camps is:

400

rods

250

rods

87.5

rods

200

rods

none of these

Answer: E

Concepts:coordinate geometry Pythagorean theorem equidistance

Difficulty rating: 1470

Small hint:

The perpendicular and camp-to-camp distances form a

300

-

400

-

500

right triangle

Big hint:

Place the camps at

(0,300)

and

(400,0)

, and put the canteen at

(t,0)

Solution:

Let the foot of the perpendicular from the girls’ camp be

(0,0).

The camps can be placed at

G=(0,300)

and

B=(400,0).

If the canteen is

C=(t,0),

equidistance gives

t^2+300^2=(400-t)^2,

so

t=87.5.

The common distance is

BC=400-87.5=312.5

rods, which is not listed.

Thus, the correct answer is E.

1953 AMC 12 Problem 41

Answer: E

Difficulty rating: 1470

Small hint:

Big hint:

Solution:

Problem 41 in other years