To find the total distance between the two cities, we'll need to calculate the distance traveled at each speed and then sum these distances.

Step 1: Convert minutes to hours

• 20 minutes at 75 km/hr:
  $\text{Time in hours} = \frac{20}{60} = \frac{1}{3} \text{ hours}$

• 17 minutes at 100 km/hr:
  $\text{Time in hours} = \frac{17}{60} \text{ hours}$

• 47 minutes at 44 km/hr:
  $\text{Time in hours} = \frac{47}{60} \text{ hours}$

Step 2: Calculate the distance for each segment

• Distance for the first segment: $\text{Distance} = 75 \, \text{km/hr} \times \frac{1}{3} \, \text{hr} = 25 \, \text{km}$

• Distance for the second segment: $\text{Distance} = 100 \, \text{km/hr} \times \frac{17}{60} \, \text{hr} \approx 28.33 \, \text{km}$

• Distance for the third segment: $\text{Distance} = 44 \, \text{km/hr} \times \frac{47}{60} \, \text{hr} \approx 34.47 \, \text{km}$

Step 3: Sum the distances

$\text{Total Distance} = 25 \, \text{km} + 28.33 \, \text{km} + 34.47 \, \text{km} \approx 87.8 \, \text{km}$

The total distance between the two cities is approximately 87.8 km.

Do you have any questions, or would you like further details?

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1. How do you convert minutes into hours?
2. How do you calculate distance if speed and time are given?
3. What is the significance of adding up distances in different segments of a journey?
4. How would the problem change if the time spent during lunch was included in the travel time?
5. What would be the effect on the total distance if one segment was traveled at a different speed?

Tip: Always ensure time is converted to the same unit when calculating distance, especially when dealing with speeds given in km/hr.