Let $d$ be the distance (in miles) Sarah walked in one direction.

Step 1: Time for each part of the trip

• Time taken to walk north (at 3 mph): $\frac{d}{3}$ hours.
• Time taken to return south (at 4 mph): $\frac{d}{4}$ hours.

Step 2: Total time for the round trip

The total time for the round trip is the sum of these two times. According to the problem, the total time was 3.5 hours, so we set up the equation: $\frac{d}{3} + \frac{d}{4} = 3.5$

Step 3: Solve for $d$

To solve this equation, we first find a common denominator for the fractions: $\frac{d}{3} + \frac{d}{4} = \frac{4d}{12} + \frac{3d}{12} = \frac{7d}{12}$

Now, solve the equation: $\frac{7d}{12} = 3.5$ Multiply both sides by 12: $7d = 3.5 \times 12$ $7d = 42$ Now divide by 7: $d = 6$

Step 4: Conclusion

Sarah walked 6 miles in one direction, so the total round trip distance was $6 + 6 = 12$ miles.

Would you like more details, or do you have any questions?

Related questions:

1. What would the total time be if she walked north at 4 mph and returned at 3 mph?
2. How would the total time change if she walked both ways at the same speed of 3 mph?
3. What if the total round trip time was 4 hours? How far would she have walked?
4. How would her total walking distance change if her speeds were halved for both directions?
5. Can we derive a general formula for the total distance based on time and speed?

Tip:

When dealing with time, distance, and speed problems, use the formula $\text{time} = \frac{\text{distance}}{\text{speed}}$ to set up equations and solve for unknowns.