Which hand has covered more distance from the 12 on a clock, the minute hand at 4:00 or the second hand at 15 seconds past? Write a fraction inequality to support your answer.
To determine which hand has covered more distance, we need to calculate how far each hand has moved from the 12 on a clock.
The minute hand moves 360 degrees in 60 minutes, which means it moves 6 degrees per minute.
At 4:00, the minute hand has moved for 4 minutes, so it has covered a distance of 4 minutes × 6 degrees/minute = 24 degrees.
The second hand moves 360 degrees in 60 seconds, which means it moves 6 degrees per second.
At 15 seconds past, the second hand has moved for 15 seconds × 6 degrees/second = 90 degrees.
To determine which hand has covered more distance, we can compare these values using a fraction inequality.
Let's represent the distance covered by the minute hand as M and the distance covered by the second hand as S.
The fraction inequality to support our answer would be:
M > S
Substituting the values we calculated:
24 degrees > 90 degrees
So, the fraction inequality to support the answer is:
24/360 > 90/360