Question

Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point Q. Two insects start crawling at the same time from point Q: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point Q?

(A) 15 minutes
(B) 30 minutes
(C) 40 minutes
(D) 1 hour
(E) 1 hour, 20 minutes

Answer 1

(E) 1hr 20 mins

Explanation:

Radius of the larger circle = 10 inches

Radius of the smaller circle = 4 inches

Circumference of a circle = 2πr

For the larger circle, circumference = 2π(10)

=20π

For the smaller circle, circumference = 2π(4)

= 8π

Rate of larger circle = 3π inches /min

Rate of smaller circle = 2.5π inches/min

For the larger circle, it will take 20π/3π

= 20/3 mins to make one revolution

For the smaller circle, it will take 8π/2.5π

= 16/5 mins to make one revolution

To find the time taken for them to bisect, find the LCM of both times. Get the denominators of both numbers equal to the other.

20/ 3 = 100/15

16/5 = 48/15

The LCM of 48 and 100 = 1200

48 = 2*2*2*2*3

100 = 2*2*5*5

LCM = 2*2*2*2*3*5*5

= 1200

So we have 1200/15 = 80 mins

= 60 mins + 20mins

= 1 hr 20 mins