Bus A and Bus B leave the bus depot at 8 am. Bus A takes 25 minutes to complete its route once and bus B takes 35 minutes to complete its route once.
If both buses continue to repeat their route, at what time will they be back at the bus depot together?
Assume the buses have no breaks in between routes.
Give your answer as a 12-hour clock time. plese help me quickly.

bus A takes 25 mins

bus B takes 35 mins

start at 8am

to find =lcm of 25 and 35

LCM of 25 and 35

5 /__25,35

/__5,7

LCM=5×5×7

=175 mins=8hr+175mins=10:55am

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.

you can't solve x because it is 2 linear equation and you only have one equation