Machines a and t were both cleaned this week machine a is cleaned every 15 weeks and machine t is cleaned every 12 weeks what is the fewest number of weeks that will pass before both machines are cleaned again in the same week. show work lcm

60 weeks

Step-by-step explanation:

Factor both numbers 12 and 15:

Find LCM(12,15). The common factor is only 3, multiply ths common factor by all factors that remain. Then

This means that the fewest number of weeks that will pass before both machines are cleaned again in the same week is 60 weeks.

4 puzzles in 3 hours

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."