You can walk 4.4 feet per second. how many minutes will it take you to get to room 117?

This problem is incomplete, I think the figure is needed. Assuming that the figure I found is correct, therefore the distance we need to walk from room 103 to 117 is:

distance = 86 ft – 22 ft = 64 ft

We can calculate for time using the formula:

time = distance / speed

time = 64 ft / (4.4 ft / second)

time = 14.55 seconds

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.