Every year, a dog sled race is held in Alaska and is approximately 1,150 miles in distance. Information about the top three racers is listed below.
Aaron completed half the race in approximately 4 days, 12 hours.
Dallas finished the race in approximately 8 days, 18 hours.
Mitch completed one-quarter of the race in approximately 2 days, 5 hours.
Based on the statements above, select all true responses where x is hours and y is miles. Assume each racer maintains the same pace throughout the race.
The equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.42x.
The equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.32x.
The equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x.
The equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.42x.
The equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.48x.
The equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.32x.
The equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.42x.
The equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x.
The equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.42x.
explain
To determine whether each equation is true, we need to compare the given information about each racer's time and distance to the equation.
For Aaron, it is stated that he completed half the race in approximately 4 days, 12 hours. This means that in 4 days, 12 hours (or 108 hours), he traveled half the distance of the race, which is 575 miles (half of 1150). Dividing the distance by the time gives us a rate of approximately 5.32 miles per hour.
Therefore, the equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.32x. This is not the same as y = 5.42x, so the statement "The equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.42x" is false.
Similarly, for Dallas, it is stated that he finished the race in approximately 8 days, 18 hours. This means he covered 1150 miles in 8 days, 18 hours (or 210 hours). Dividing the distance by the time gives us a rate of approximately 5.48 miles per hour.
Therefore, the equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x, which matches the given equation. So, the statement "The equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x" is true.
For Mitch, it is stated that he completed one-quarter of the race in approximately 2 days, 5 hours. This means he covered one-quarter of the distance, which is 287.5 miles (one-quarter of 1150), in 2 days, 5 hours (or 53 hours). Dividing the distance by the time gives us a rate of approximately 5.42 miles per hour.
Therefore, the equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.42x, which matches the given equation. So, the statement "The equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.42x" is true.
Therefore, the correct statements are:
- The equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x.
- The equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.42x.
To find the equation that represents the approximate distance traveled over time for each racer, we can use the information provided.
Let's start with Aaron's dog sled team. According to the information, Aaron completed half the race in approximately 4 days, 12 hours. To find the rate at which they travel, we can divide the distance (y) by the time (x). Since Aaron completed half the race, the distance would be (1/2)*(1150 miles) = 575 miles. And the time would be (4.5 days)*(24 hours/day) = 108 hours. So, the rate can be calculated as (575 miles) / (108 hours) ≈ 5.32 miles/hour.
Therefore, the equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.32x.
Let's move on to Dallas' dog sled team. According to the information, Dallas finished the race in approximately 8 days, 18 hours. Again, to find the rate, we divide the distance by the time. The distance would be the full race distance, which is 1150 miles. The time would be (8.75 days) * (24 hours/day) = 210 hours. So, the rate is (1150 miles) / (210 hours) ≈ 5.48 miles/hour.
Therefore, the equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x.
Finally, let's consider Mitch's dog sled team. According to the information, Mitch completed one-quarter of the race in approximately 2 days, 5 hours. The distance would be one-quarter of the full race distance, which is (1/4)*(1150 miles) = 287.5 miles. The time would be (2.0833 days) * (24 hours/day) = 50 hours. So, the rate is (287.5 miles) / (50 hours) ≈ 5.75 miles/hour.
Therefore, the equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.75x.
Based on the calculations, the correct statements are:
- The equation that represents the approximate distance Aaron's dog sled team travels over time is y = 5.32x.
- The equation that represents the approximate distance Dallas' dog sled team travels over time is y = 5.48x.
- The equation that represents the approximate distance Mitch's dog sled team travels over time is y = 5.75x.