someone please help?

Question

1. How many times between 12 noon and 12 midnight do the minute and hour hands of a clcok line up exactly?
A. 10
B. 11
C. 12
D. 23
E. 24

2. The instruction on a can of oragnage juice concentrate state that the water should be mixed with the concentrate in the ratio of 3 to 1. If 12 liters of orange juice are needed, how many liters of concentrate need to be bought?

3. In a prehistoric village, rocks, stones, and pebbles were used as money. The relative values of the "coins" were:
1 rock= 7 stones
1 rock= 49 pebbles
If a man used 6 rocks to puchase a hide that cost 5 rocks, 2 stones, and 3 pebbles, how many change was he owed?

4. A job can be done in 25 hrs. by 6 people. How many people would be needed to do the same job in 8 or fewer hours?

Answer 1

1. (A) 10.
Around 1:06, 2:11, 3:17, 4:22, 5:28, 6:33, 7:39, 8:44, 9:49, 10:54.

The "trick" is to realize that in the 11:00 hour the hands don't actually line up until midnight, which is not counted.

The question say "BETWEEN" noon and midnight, so it is pretty clear (to me) that neither noon nor midnight is counted.

2. 3:1 ratio of water to concentrate. If you want 12 liters of orange juice, you'd want 9 liters of water to 3 liters of concentrate.

The problem is done this way: the total volume of juice is the volume of water plus the volume of concentrate. If we use x liters of concentrate, then:

x + 3x = 12
4x = 12
x = 3

3 liters of concentrate, then 9 of water.

3. 4 stones and 4 pebbles.

Convert his 6th rock to 7 stones. Convert one of the 7 stones to 7 pebbles, leaving 6 stones. Then he pays 5-6-7 for something that costs 5-2-3. 6-2 = 4 stones, 7-3 = 4 pebbles.

This is just like doing subtraction in base-10.

4. 25 hours by 6 people means that the job takes 25*6 = 150 people-hours.

To do it in 8 hours, you'd need 150/8 people, which is 18.75.

Rounding up, 19 people is the smallest number that would complete in 8 hours or less.

18 people = 150/18 hours = 8.33 hours
19 people = 150/19 hours = 7.89 hours

Answer 2

1)11 times if 12:00 is counted

I derived a formula:

M = 60 * H/11

Where M = Minutes past H when both hands of the clock intersect.

H = Hour ie 1,2,3,4,5,6,7....12

Using this, for example we can find that for H=10, we get Time is M = 60 * 10/11 = 54 minutes

*****ie 10:54 ***

Another example: H = 11 hrs

M = 60 * 11/11 = 60 minutes!!
This means 12:00. This is the proof that the formula is right

2) 12 litres of juice needed.

3:1 ratio for water : concentrate

so 1/4 is concentrate = 3 litres
water is 9 litres ( 9 + 3 = 12)

4) one person will do the job in 150 hrs. so in order to do in 8 hrs, people needed = 150/8 = 18.75 (19 people)

Answer 3

A. 11 - the hour hand goes around once and the minute hand 12 times, so it must overtake the hour hand 11 times. Though it depends whether you include one, both or neither of the endpoints - I'm assuming one in this answer.

2. 3 litres - mixed with 9L of water this will make 12L of juice.

3. 4 stones and 4 pebbles.

4. It takes 6×25 = 150 person-hours to do, so we need at least 150/8 = 18.75 people, i.e. 19 people or more.

Answer 4

The first question is 12....they line up at 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155 and 12

Answer 5

do your own homework lil girl!