Question

The second hand on a clock is 2.5" long.

How far does the tip of the second hand move in 3 minutes and 13 seconds?

Answer 1

interesting question. First, if it went all the way round (1 full circle) how far did it go ?

Answer 2

it did not go all the way around the clock.

Answer 3

I know, but the first step could be
figure out how big a circle it makes, if it did go all the way around

Answer 4

Do you remember how to find the size of a circle, if you know its radius ?

Answer 5

2*pi*r

Answer 6

yes, with r = 2.5 inches (then length of the second hand)

C (for circumference) = 2*pi*2.5= 5 pi
(no need to replace pi with 3.14159.... yet)

How long does it take the second hand to go all the way around ?

Answer 7

43200?

Answer 8

seconds

Answer 9

43200 what ?

Have you ever seen a second hand go around ? I think it takes exactly 60 seconds (or exactly 1 minute) to go around once.

Answer 10

See the first paragraph
http://en.wikipedia.org/wiki/Clock_face
for a description of a clock with hands.

Answer 11

is the answer 49.1?

Answer 12

If the second hand goes around once in 1 minute, it traveled 5 pi inches

Now to answer the question.
How far does the tip of the second hand move in 3 minutes and 13 seconds?

How far does it go in exactly 3 minutes ?

Answer 13

If it goes 5*pi in 1 minute, how far does it go in 3 minutes ?

Answer 14

15 pi

Answer 15

ok, now for the 13 seconds

13 seconds is part of a minute. Can you change 13 seconds to a fraction of a minute ?

Answer 16

yes i can. is the answer 1.7 inches??

Answer 17

I would change 13 seconds to 13/60 of a minute

or 0.217 minutes (roughly, as a decimal)

the clock goes 5*pi*0.217 inches more or 1.085 pi more

together with the 15 pi we get
15 pi + 1.085 pi = 16.085 pi

(or we could have done 3 minutes and 13 seconds is 3.217 minutes, and total distance is 5*pi*3.217 which is 16.085*pi inches)

now it's time to multiply by 3.14 (pi , roughly)

Answer 18

Thank you so much for you help and persistence. This is a difficult subject for me. I wil be back later to work on this.

Answer 19

Hopefully you get 16.085*3.14= 50.5 inches

if you use the pi key on your calculator, you should find
(3+13/60)*2*pi*2.5= 50.5272818