Andre rose his bicycle to a park located 5 1/2 miles from his house. He returned along the same route. After riding 7 1/3 miles total, how many more miles does Andre need to ride to reach his home?
(2 * 5 1/2) - 7 1/3 = ?
Andre is cycling his to the coffee shop. His house and the coffee shop are both 2 miles from the town square. The bike path starts on Main Street halfway between his house and the town square . The path ends on North Street, three-quarters of the way from the town square to the coffee shop. Andre rides at an average rate of 15 miles per hour. To the nearest minute, how much time will he save if he takes the bike path instead of riding through the town square? Explain.
To find out how many more miles Andre needs to ride to reach his home, we need to subtract the distance he has already ridden from the total distance between his house and the park.
Andre rode 7 1/3 miles in total, which includes both going to the park and returning. The distance between his house and the park is 5 1/2 miles.
To find the remaining distance, we'll subtract the distance Andre has already ridden from the total distance between his house and the park:
Total distance - Distance already ridden = Remaining distance
5 1/2 miles - 7 1/3 miles = Remaining distance
To subtract mixed numbers, we need to convert them to improper fractions.
5 1/2 = 11/2 (denominator multiplied by the whole number and added to the numerator)
7 1/3 = 22/3 (denominator multiplied by the whole number and added to the numerator)
Now, we can subtract the fractions:
11/2 - 22/3 = Remaining distance
To subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 2 and 3 is 6.
11/2 = (11 * 3) / (2 * 3) = 33/6
22/3 = (22 * 2) / (3 * 2) = 44/6
Now we can subtract:
33/6 - 44/6 = -11/6
The remaining distance is -11/6 miles. Since it doesn't make sense to have a negative distance, we can conclude that Andre has already ridden more than the distance between his house and the park.
To find out how many more miles Andre needs to ride to reach his home, we can subtract the distance he has already ridden from the total distance between his house and the park.
We know that Andre rode a total of 7 1/3 miles. We also know that the park is located 5 1/2 miles from his house.
To subtract these distances, we'll convert the mixed numbers (7 1/3 and 5 1/2) into improper fractions.
7 1/3 can be written as (7 * 3/3) + 1/3 = 21/3 + 1/3 = 22/3
5 1/2 can be written as (5 * 2/2) + 1/2 = 10/2 + 1/2 = 11/2
Now, we can subtract 22/3 (the distance Andre has already ridden) from 11/2 (the total distance between the house and the park) to find out how many more miles he needs to ride.
11/2 - 22/3 = (11 * 3) / (2 * 3) - (22 * 2) / (3 * 2) = 33/6 - 44/6 = (33 - 44) / 6 = -11/6
The result, -11/6, tells us that Andre has already ridden 11/6 miles more than the total distance between his house and the park. Since we are looking for the remaining distance, we need to take the absolute value of -11/6, which is 11/6.
Therefore, Andre still needs to ride 11/6 (or 1 5/6) miles to reach his home.