A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 20 min at 75 km/hr, 17 min at 100 km/hr, and 47 min at 44 km/hr. She spends 24 min eating lunch and buying gas. 

What is the distance between the two cities?

(Remember to convert between minutes and hours.)

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?

---

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.

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 20 min at 75 km/hr, 17 min at 100 km/hr, and 47 min at 44 km/hr. She spends 24 min eating lunch and buying gas. What is the distance between the two cities? (Remember to convert between minutes and hours.)

Learn how to calculate the total distance between two cities based on different driving speeds. This problem covers key mathematical concepts such as distance calculation, speed-time-distance relationships, and unit conversion. Suitable for students in Grades 6-8.

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