Explain why a kid who runs 3/4 mile in 6 minutes is faster than a kid who runs 1/2 mile in 5 minutes?
(3/4) mile / 6 min = 3/24 = 1/8 mile/min = 0.125 mile/min
(1/2) mile /5 min = 1/10 mile / min = 0.100 mile/min
because
To determine which kid is faster, we can compare their running speeds, which are expressed as distance per unit of time. In this case, the first kid runs 3/4 mile in 6 minutes, while the second kid runs 1/2 mile in 5 minutes.
To compare their running speeds, we can calculate the distance each kid covers per minute. Let's start with the first kid:
The first kid runs 3/4 mile in 6 minutes. We divide the distance by the time:
(3/4) mile ÷ 6 minutes = (3/4) ÷ 6 = 3/4 × 1/6 = 3/24 = 1/8 mile per minute.
Now, let's calculate the second kid's running speed:
The second kid runs 1/2 mile in 5 minutes:
(1/2) mile ÷ 5 minutes = (1/2) ÷ 5 = 1/2 × 1/5 = 1/10 mile per minute.
Comparing the two speeds, we can see that the first kid runs at a faster pace, covering 1/8 mile per minute, while the second kid covers 1/10 mile per minute. Therefore, the kid who runs 3/4 mile in 6 minutes is faster than the kid who runs 1/2 mile in 5 minutes.
To determine which kid is faster, we need to compare their running speeds. To do this, we can calculate their individual speed by dividing the distance they run by the time it takes them.
First, let's calculate the speed of the kid who runs 3/4 mile in 6 minutes:
Speed = Distance / Time
Speed = (3/4) mile / 6 minutes
To make the calculation easier, we'll convert the distance and time to a common unit. Let's convert the distance to the same unit as the time, such as minutes.
(3/4) mile = (3/4) mile × (8/8) = (3/4) × (8/8) = 6/8 mile
Now that we have the distance in the same unit as time, we can calculate the speed:
Speed = (6/8) mile / 6 minutes
Speed = (6/8) / 6
Speed = (6/8) × (1/6)
Speed = 1/8 mile per minute
Now let's calculate the speed of the kid who runs 1/2 mile in 5 minutes:
Speed = Distance / Time
Speed = (1/2) mile / 5 minutes
Again, we'll convert the distance to the same unit as the time:
(1/2) mile = (1/2) mile × (10/10) = (1/2) × (10/10) = 5/10 mile
Now we can calculate the speed:
Speed = (5/10) mile / 5 minutes
Speed = (5/10) / 5
Speed = (5/10) × (1/5)
Speed = 1/10 mile per minute
Comparing the two speeds, we see that the kid who runs 3/4 mile in 6 minutes has a speed of 1/8 mile per minute, while the kid who runs 1/2 mile in 5 minutes has a speed of 1/10 mile per minute.
Therefore, the kid who runs 3/4 mile in 6 minutes is faster than the kid who runs 1/2 mile in 5 minutes because their speed is higher.