Megan, Jose, Austin, and Timothy are driving from Atlanta to Orlando which is a total of four hundred miles. They each left at 6:45 a.m. Everyone has been driving at different average speeds.
Figure out the average speed of each driver.
1. Jose's friend is driving from Orlando to Atlanta at fifty-six mph. His friend started from Orlando at the same time Jose left from Atlanta. At 7:54 a.m. they will be about 260 miles apart.
2. After two hours, Timothy has car troubles and had to drive the rest of the way at an average speed which is ten mph slower than his average speed for the first two hours. At 2:50 p.m. Timothy arrived in Orlando.
3. Austin drove at an average speed that was eight mph faster than Megan. Austin arrived in Orlando at 1:05 p.m.
Idk I'm stuck
To find the average speed of each driver, we can use the formula:
Average Speed = Total Distance / Total Time
Let's calculate the average speed for each driver using the given information:
1. Jose's friend is driving from Orlando to Atlanta at fifty-six mph. At 7:54 a.m. they will be about 260 miles apart.
Distance traveled by Jose's friend = 260 miles
Time taken = 7:54 a.m. - 6:45 a.m. = 1 hour and 9 minutes = 1.15 hours
Average Speed of Jose's friend = 260 miles / 1.15 hours ≈ 226.09 mph
2. After two hours, Timothy has car troubles and had to drive the rest of the way at an average speed which is ten mph slower than his average speed for the first two hours. Timothy arrived in Orlando at 2:50 p.m.
Time taken for the first two hours = 2 hours (given)
Time taken for the rest of the way = 2:50 p.m. - 6:45 a.m. - 2 hours = 6 hours and 5 minutes = 6.08 hours
Let Timothy's average speed for the first two hours be x mph.
Average Speed for the rest of the way = (x - 10) mph
Distance traveled for the first two hours = x mph * 2 hours = 2x miles
Distance traveled for the rest of the way = (x - 10) mph * 6.08 hours = 6.08x - 60.8 miles
Total distance traveled = Distance for the first two hours + Distance for the rest of the way = 2x + 6.08x - 60.8 miles
Total distance traveled = 400 miles (given)
2x + 6.08x - 60.8 = 400
8.08x - 60.8 = 400
8.08x = 460.8
x ≈ 57.02 mph
Average Speed of Timothy for the first two hours = x ≈ 57.02 mph
Average Speed of Timothy for the rest of the way = x - 10 ≈ 57.02 - 10 ≈ 47.02 mph
3. Austin drove at an average speed that was eight mph faster than Megan. Austin arrived in Orlando at 1:05 p.m.
Time taken by Austin = 1:05 p.m. - 6:45 a.m. = 6 hours and 20 minutes = 6.33 hours
Let Megan's average speed be m mph.
Average Speed of Austin = (m + 8) mph
Distance traveled = Average Speed * Time taken = (m + 8) mph * 6.33 hours
Total distance traveled = Distance traveled = 400 miles (given)
(m + 8) mph * 6.33 hours = 400
6.33m + 50.64 = 400
6.33m = 349.36
m ≈ 55.16 mph
Average Speed of Megan = m ≈ 55.16 mph
Therefore, the average speeds of each driver are:
Jose's friend: Approx. 226.09 mph
Timothy (first two hours): Approx. 57.02 mph
Timothy (rest of the way): Approx. 47.02 mph
Austin: Approx. 55.16 mph