-A clock is divided equally into 60 units. Each unit forms an angle of 6^0.The hour hand moves 1 of these units for every 12 units that the minute hand moves. it move 2 of these units for every 24 units for the minute hand,ete.At 6 o'clock the hour hand and the minute hand are 30 units apart or 6x30=180^0. At 6:36 what angle would the two hand form?

* Two cars 100 miles apart are traveling toward each other at constant speeds of 50m.p.h. and 40m.p.h. In one hour(60 minutes), their positions will be 10 miles apart. They will then pass each other, going in opposite directions and come to positions again that are 10 miles apart. How many minutes and seconds wiil it take to go from their first positions of 10 miles apart to their second positions of 10 miles apart?

To find the angle formed by the hour and minute hands at 6:36, we need to determine the positions of both hands.

At 6 o'clock, the hour hand is pointing at the 6 and the minute hand is pointing at the 12. In terms of the units mentioned, the hour hand is at 30 units (6x6=30) and the minute hand is at 0 units.

We know that the hour hand moves 1 unit for every 12 units that the minute hand moves. Therefore, for every 12 units the minute hand moves, the hour hand moves 1 unit. In this case, the minute hand moved from 0 units to 36 units (6x6=36), so the hour hand has moved 3 units (36 divided by 12).

Therefore, at 6:36, the hour hand is at 33 units (30+3) and the minute hand is at 36 units.

To find the angle between the two hands, we calculate the difference between their positions: 36 units - 33 units = 3 units.

Since each unit forms an angle of 6 degrees, the angle formed at 6:36 is 3 units x 6 degrees/unit = 18 degrees.

So, at 6:36, the angle between the hour and minute hands is 18 degrees.

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The two cars are traveling towards each other at speeds of 50 mph and 40 mph, respectively. In one hour (60 minutes), their positions will be 10 miles apart.

Since their positions change by 10 miles in 60 minutes, the relative speed of the two cars is 50 mph + 40 mph = 90 mph.

To find how many minutes and seconds it will take them to go from their first positions of 10 miles apart to their second positions of 10 miles apart, we need to divide the distance (10 miles) by their relative speed (90 mph), and convert the result into minutes and seconds.

10 miles / 90 mph = 0.1111 hours

Since there are 60 minutes in an hour, we multiply 0.1111 hours by 60 minutes/hour to convert it into minutes:

0.1111 hours x 60 minutes/hour = 6.67 minutes

Therefore, it will take approximately 6 minutes and 40 seconds (0.67 minutes x 60 seconds/minute = 40 seconds) for the two cars to go from their first positions of 10 miles apart to their second positions of 10 miles apart.

To find the angle formed by the hour and minute hand at 6:36, we can use the following steps:

1. Identify the positions of the hour and minute hand at 6 o'clock:
- The hour hand is pointing directly at the number 6, which corresponds to 180°.
- The minute hand is pointing at the number 12, which corresponds to 0°.

2. Calculate the distance covered by the hour hand from 6 o'clock to 6:36:
- The hour hand moves 1 unit for every 12 units the minute hand moves.
- From 6 to 6:36, the minute hand has covered 36 units.
- Therefore, the hour hand has covered 36/12 = 3 units.

3. Calculate the new position of the hour hand at 6:36:
- Since each unit forms an angle of 6°, the hour hand has moved 3 x 6° = 18°.

4. Calculate the new position of the minute hand at 6:36:
- The minute hand has moved 36 x 6° = 216° from 12 (starting position) to 6:36.

5. Calculate the angle between the hour and minute hand at 6:36:
- The minute hand is at 216° and the hour hand is at 180° + 18° = 198°.
- The angle between the hour and minute hand is 216° - 198° = 18°.

Therefore, at 6:36, the hour and minute hand form an angle of 18°.

For the second question, let's calculate the time taken to go from their first positions to their second positions:

1. The cars are initially 100 miles apart.

2. The relative speed of the two cars is the sum of their individual speeds, which is 50 mph + 40 mph = 90 mph.

3. In one hour (60 minutes), the cars will cover a distance of 90 miles.

4. It is given that in 60 minutes, their positions will be 10 miles apart. This means they will have covered 90 - 10 = 80 miles relative to each other.

5. Therefore, it takes 60 minutes to cover 80 miles relative to each other.

To calculate the time taken in minutes and seconds, we can use the formula:

Time (in minutes) = Distance / Speed
Time (in seconds) = Time (in minutes) x 60

6. Substituting the values:
Time (in minutes) = 80 miles / 90 mph = 8/9 hour = 8/9 x 60 minutes = 53.3 minutes.

7. To convert minutes to seconds, multiply by 60:
Time (in seconds) = 53.3 minutes x 60 = 3198 seconds.

Therefore, it will take approximately 53 minutes and 18 seconds to go from their first positions of 10 miles apart to their second positions of 10 miles apart.