**at noon the minute and the hour hands overlap. when will it happen next?

1 hour and 60/11 minutes.

Explanation:

How many degrees the Minute Hand Travels in 1 minute: 6º

How many degrees the Hour Hand Travels in 1 minute: 0.5º

If x is the number of minutes the clock traveled after 1 o'clock to reach the next meeting point,

The degrees that the minute hand traveled is 6 * x = 6xº

The degrees that the hour hand traveled is 0.5 * x = 0.5xº

In 12 hours the hour hand travels 360º,

So, in 1 hour, it travels 30º

Total number of degrees the clock traveled after 1 o'clock to reach the next meeting point,

6x = 30 + 0.5x

6x because the minute hand starts at the beginning.

30 because that counts for the number of degrees covered until 1 o'clock.

0.5x because that counts for the number of degrees the hour hand travels after 1 o'clock.

6x = 30 + 0.5x

5.5x = 30

55x = 300

x = 300/55 = 60/11

If you add back that one hour, then it becomes 1 hour and 60/11 minutes.

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.