On rainy days, Izzy goes from his house to the school by running 1.2 miles on West St, then makes a 90º turn and runs 0.5 miles on North Ave.
a. If Izzy runs 7.5 miles per hour, approximately how much time will it take her to run to school on rainy days?
b. On dry days, Izzy runs on the dashed path through the woods. How far is she traveling?
c. If Izzy runs 7.5 miles per hour, how much time will she save by cutting through the woods?
time = distance/speed, so
(a) (1.2 + 0.5)/7.5 = 0.22666 hrs or 13.6 minutes
(b) √(1.2^2+0.5^2) = 1.3 miles
(c) figure the time for (b) and then subtract from (a).
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a. To calculate the time it will take Izzy to run to school on rainy days, we need to find the total distance she runs and then divide it by her speed.
The distance she runs is the sum of the distances on West St and North Ave:
Distance = 1.2 miles + 0.5 miles = 1.7 miles
Now, we divide the distance by her speed to find the time:
Time = Distance / Speed = 1.7 miles / 7.5 miles per hour
Using a calculator, we can find the time to be 0.2267 hours.
b. To determine the distance Izzy travels on dry days, we need to calculate the hypotenuse of the right-angled triangle formed by West St and North Ave.
Using the Pythagorean theorem, we have:
Distance = √(1.2^2 + 0.5^2)
Simplifying the equation gives us:
Distance = √(1.44 + 0.25)
Distance = √1.69
Using a calculator or estimation, the distance is approximately 1.30 miles.
c. To find the time saved by cutting through the woods, we need to compare the time taken to travel on rainy days with the time taken on dry days.
On rainy days, the time taken is calculated as 0.2267 hours.
To find the time taken on dry days, we divide the distance by the speed:
Time = Distance / Speed = 1.30 miles / 7.5 miles per hour
Using a calculator, we can find the time taken on dry days to be 0.1733 hours.
To find the time saved, we subtract the time taken on dry days from the time taken on rainy days:
Time saved = Time on rainy days - Time on dry days = 0.2267 hours - 0.1733 hours
Using a calculator, we can find that Izzy saves approximately 0.0533 hours, or 3.2 minutes, by cutting through the woods.
To solve these problems, we need to find the time it takes for Izzy to travel each distance, using the formula: time = distance / speed.
a. To find the time it takes for Izzy to run to school on rainy days, we add the distances traveled on West St and North Ave: 1.2 miles + 0.5 miles = 1.7 miles.
Time taken = 1.7 miles / 7.5 miles per hour ≈ 0.227 hours.
To convert this to minutes, multiply by 60 (since there are 60 minutes in an hour): 0.227 hours * 60 minutes/hour ≈ 13.62 minutes.
So, it will take Izzy approximately 13.62 minutes to run to school on rainy days.
b. To find the distance Izzy travels through the woods on dry days, we need to determine the length of the dashed path. However, the length of the dashed path is not provided in the question. Please provide the length of the dashed path to solve this part of the question.
c. To find the time saved by cutting through the woods, we need to calculate the time it takes for Izzy to run on the dashed path through the woods and subtract it from the time it takes for her to run on West St and North Ave. However, since we don't have the distance of the dashed path in this question, we cannot determine the time saved.