Andre is cycling from his house 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 Andre’s house and the
town square. The path ends on
North Street, __
3
4 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?
To solve this problem, we need to first calculate the distance that Andre saves by taking the bike path instead of riding through the town square.
The distance between Andre's house and the town square is 2 miles, so the distance from the bike path's starting point to Andre's house is also 2 miles. Similarly, the distance between the coffee shop and the town square is also 2 miles, so the distance from the bike path's end point to the coffee shop is (3/4) x 2 = 1.5 miles.
Therefore, by taking the bike path, Andre saves 2 + 1.5 = 3.5 miles.
Next, we can calculate the time it takes for Andre to ride this distance at 15 miles per hour:
time = distance / rate = 3.5 / 15 = 0.2333 hours
To convert this to minutes, we multiply by 60:
time = 0.2333 x 60 ≈ 14 minutes
Therefore, Andre will save approximately 14 minutes by taking the bike path instead of riding through the town square.
Oh, boy! Let's do some math, but I promise to keep it fun! So, Andre's house and the coffee shop are both 2 miles away from the town square. Now, the bike path starts on Main Street, halfway between Andre's house and the town square.
According to my circus-calculator, that means Andre has to travel 1 mile from his house to the bike path, then another mile from the bike path to the town square. That's a total of 2 miles to reach the town square by riding through it.
Now, the bike path ends on North Street, which is 3/4 (or 0.75) of the way from the town square to the coffee shop.
So, let's calculate how much Andre needs to ride if he takes the bike path. If the distance from the town square to the coffee shop is 2 miles, then Andre only needs to ride 0.75 * 2 = 1.5 miles on the bike path to reach the coffee shop.
Now, let's find out how much time it takes Andre to ride these distances. Since Andre rides at an average rate of 15 miles per hour, it would take him 2 / 15 = 0.1333... hours to ride through the town square.
On the bike path, Andre only needs to ride 1.5 / 15 = 0.1 hours to reach the coffee shop.
To convert this into minutes, we know that there are 60 minutes in an hour. So, 0.1 hours is equal to 0.1 * 60 = 6 minutes.
So, Andre would save approximately 6 minutes if he takes the bike path instead of riding through the town square.
To calculate the time saved by taking the bike path, we need to compare the time it takes to ride through the town square with the time it takes to ride on the bike path.
First, let's calculate the distance Andre would have to ride if he goes through the town square. Since his house and the coffee shop are both 2 miles from the town square, the total distance he would have to ride is 2 miles + 2 miles = 4 miles.
Now, let's calculate the time it would take Andre to ride this distance. Andre rides at an average rate of 15 miles per hour, so we divide the distance by the rate to find the time: 4 miles / 15 miles per hour = 0.267 hours.
To convert this time to minutes, we multiply by 60: 0.267 hours * 60 minutes per hour = 16.02 minutes. Rounding to the nearest minute, Andre would take approximately 16 minutes if he rides through the town square.
Now, let's calculate the distance Andre would have to ride if he takes the bike path. The bike path ends on North Street, which is 3/4 of the way from the town square to the coffee shop. Since the town square is 2 miles from both the house and the coffee shop, 3/4 of this distance is 3/4 * 2 miles = 1.5 miles.
To calculate the total distance Andre would have to ride on the bike path, we add the distance from the house to the bike path (1.5 miles) and the distance from the bike path to the coffee shop (2 miles): 1.5 miles + 2 miles = 3.5 miles.
Now, let's calculate the time it would take Andre to ride this distance. Again, we divide the distance by his average rate: 3.5 miles / 15 miles per hour = 0.233 hours.
Multiplying by 60, we get: 0.233 hours * 60 minutes per hour = 13.98 minutes. Rounding to the nearest minute, Andre would take approximately 14 minutes if he takes the bike path.
To find the time saved, we subtract the time it takes to ride on the bike path from the time it takes to ride through the town square: 16 minutes - 14 minutes = 2 minutes.
Therefore, to the nearest minute, Andre would save approximately 2 minutes if he takes the bike path instead of riding through the town square.
To find out how much time Andre will save by taking the bike path instead of riding through the town square, we need to compare the distances and speeds of the two routes.
Let's first calculate the distance Andre would have to travel if he rides through the town square. Since his house and the coffee shop are both 2 miles from the town square, the total distance he would have to travel is 2 + 2 = 4 miles.
Now, let's calculate the distance Andre would have to travel if he takes the bike path. The bike path starts on Main Street, halfway between Andre’s house and the town square, so he would have to travel 2 / 2 = 1 mile to reach the start of the bike path. The path ends on North Street, 3/4 of the way from the town square to the coffee shop, so the distance he would have to travel on the bike path is (3/4) * 2 = 1.5 miles.
Next, let's calculate the time it would take Andre to ride through the town square. We can use the formula: Time = Distance / Speed. Since his average speed is 15 miles per hour and the distance is 4 miles, the time it would take him is 4 / 15 = 0.267 hours.
Similarly, let's calculate the time it would take Andre to ride on the bike path. Using the same formula: Time = Distance / Speed, and with a distance of 1.5 miles, the time it would take him is 1.5 / 15 = 0.1 hours.
To find the time difference, we subtract the time it would take to ride on the bike path from the time it would take to ride through the town square: 0.267 - 0.1 = 0.167 hours.
To convert this time into minutes, we multiply by 60: 0.167 * 60 = 10.02 minutes.
Therefore, Andre would save approximately 10 minutes (to the nearest minute) by taking the bike path instead of riding through the town square.