Driving at a constant speed, you drove 14 miles in 20 minutes. On the “double number line”, show different distances and times that would give you the same speed. Use simple, logical reasoning to determine these equivalent rates.
No “double number line”. Cannot copy and paste here.
To determine the equivalent rates on a "double number line" for the given scenario, we need to find different distances and times that would give us the same speed.
First, let's convert the given time of 20 minutes to hours for easier calculations. There are 60 minutes in an hour, so 20 minutes is equivalent to 20/60 = 1/3 hours.
Now, let's calculate the speed. Speed is defined as the distance traveled divided by the time taken. In this case, the distance is 14 miles and the time is 1/3 hours.
Speed = Distance / Time
Speed = 14 miles / 1/3 hour
Speed = 14 miles * 3/1 hour
Speed = 42 miles per hour
So, the given speed is 42 miles per hour.
To find different distances and times that would give the same speed, we can use proportional reasoning. Since speed is a measure of how fast you are traveling, if the speed remains the same, the ratio of distances to times should also remain the same.
For example, if we traveled at a distance of 21 miles, the time it would take can be calculated using the speed:
Time = Distance / Speed
Time = 21 miles / 42 miles per hour
Time = 1/2 hour
Therefore, driving 21 miles at a speed of 42 miles per hour would take 1/2 hour.
Similarly, we can find other equivalent rates by maintaining the same ratio:
- Distance: 7 miles, Time: 1/6 hour (7 miles / 42 miles per hour)
- Distance: 28 miles, Time: 2/3 hours (28 miles / 42 miles per hour)
- Distance: 35 miles, Time: 5/6 hours (35 miles / 42 miles per hour)
These are just a few examples of different distances and times that would give you the same speed of 42 miles per hour. By using simple, logical reasoning and applying the concept of speed, you can find many more equivalent rates on the "double number line."