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### Problem 1: Exercise Hours
What do you know?
- Your goal is to exercise for 15 hours this month.
- You have already exercised [tex]\(3 \frac{1}{2}\)[/tex] hours in the first week.
- In the second week, you exercised [tex]\(3 \frac{3}{4}\)[/tex] hours.
What do you need to find?
- The number of more hours you need to exercise to reach your 15-hour goal.
Solution:
1. Calculate total hours exercised so far:
- First week: [tex]\(3 \frac{1}{2} = 3 + 0.5 = 3.5\)[/tex] hours
- Second week: [tex]\(3 \frac{3}{4} = 3 + 0.75 = 3.75\)[/tex] hours
- Total hours exercised = [tex]\(3.5 + 3.75 = 7.25\)[/tex] hours
2. Find out how many more hours are needed to reach the goal:
- Total goal = 15 hours
- Hours needed = Total goal - Total hours exercised
- Hours needed = [tex]\(15 - 7.25 = 7.75\)[/tex] hours
So, you need to exercise 7.75 more hours to reach your goal.
### Problem 2: Taxi Driver's Miles
What do you know?
- The taxi driver travels [tex]\(4 \frac{5}{8}\)[/tex] miles to his first stop.
- He travels [tex]\(1 \frac{3}{4}\)[/tex] miles less to the second stop.
What do you need to find?
- The total number of miles the taxi driver travels for the two stops.
Solution:
1. Convert the mixed numbers to decimals:
- First stop: [tex]\(4 \frac{5}{8} = 4 + 0.625 = 4.625\)[/tex] miles
- Decreased distance for the second stop: [tex]\(1 \frac{3}{4} = 1 + 0.75 = 1.75\)[/tex] miles
2. Calculate the distance to the second stop:
- Second stop miles = First stop distance - Decreased distance
- Second stop = [tex]\(4.625 - 1.75 = 2.875\)[/tex] miles
3. Calculate the total distance traveled:
- Total miles = First stop distance + Second stop distance
- Total miles = [tex]\(4.625 + 2.875 = 7.5\)[/tex] miles
Therefore, the taxi driver traveled 7.5 miles in total for the two stops.
### Problem 1: Exercise Hours
What do you know?
- Your goal is to exercise for 15 hours this month.
- You have already exercised [tex]\(3 \frac{1}{2}\)[/tex] hours in the first week.
- In the second week, you exercised [tex]\(3 \frac{3}{4}\)[/tex] hours.
What do you need to find?
- The number of more hours you need to exercise to reach your 15-hour goal.
Solution:
1. Calculate total hours exercised so far:
- First week: [tex]\(3 \frac{1}{2} = 3 + 0.5 = 3.5\)[/tex] hours
- Second week: [tex]\(3 \frac{3}{4} = 3 + 0.75 = 3.75\)[/tex] hours
- Total hours exercised = [tex]\(3.5 + 3.75 = 7.25\)[/tex] hours
2. Find out how many more hours are needed to reach the goal:
- Total goal = 15 hours
- Hours needed = Total goal - Total hours exercised
- Hours needed = [tex]\(15 - 7.25 = 7.75\)[/tex] hours
So, you need to exercise 7.75 more hours to reach your goal.
### Problem 2: Taxi Driver's Miles
What do you know?
- The taxi driver travels [tex]\(4 \frac{5}{8}\)[/tex] miles to his first stop.
- He travels [tex]\(1 \frac{3}{4}\)[/tex] miles less to the second stop.
What do you need to find?
- The total number of miles the taxi driver travels for the two stops.
Solution:
1. Convert the mixed numbers to decimals:
- First stop: [tex]\(4 \frac{5}{8} = 4 + 0.625 = 4.625\)[/tex] miles
- Decreased distance for the second stop: [tex]\(1 \frac{3}{4} = 1 + 0.75 = 1.75\)[/tex] miles
2. Calculate the distance to the second stop:
- Second stop miles = First stop distance - Decreased distance
- Second stop = [tex]\(4.625 - 1.75 = 2.875\)[/tex] miles
3. Calculate the total distance traveled:
- Total miles = First stop distance + Second stop distance
- Total miles = [tex]\(4.625 + 2.875 = 7.5\)[/tex] miles
Therefore, the taxi driver traveled 7.5 miles in total for the two stops.
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