Finding Uphill and Downhill Hiking Speeds Using Equal Distances
Apply the distance, rate, and time problem-solving strategy to find two unknown speeds when both modes of travel cover the same distance, requiring a unit conversion from minutes to hours.
Problem: Suzy takes 50 minutes to hike uphill from the parking lot to the lookout tower. It takes her 30 minutes to hike back down to the parking lot. Her speed going downhill is 1.2 miles per hour faster than her speed going uphill. Find Suzy's uphill and downhill speeds.
- Read and draw: The uphill and downhill distances are equal.
- Identify: The uphill and downhill hiking speeds.
- Name: Let = uphill speed in mph. Then the downhill speed is . Convert the times from minutes to hours: 50 minutes = hour, and 30 minutes = hour.
| Rate (mph) | Time (hrs) | Distance (miles) | |
|---|---|---|---|
| Uphill | |||
| Downhill |
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Translate: The uphill distance and downhill distance are exactly the same:
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Solve: Clear the fractions by multiplying both sides by the LCD, which is 6: The uphill speed is 1.8 mph. The downhill speed is mph.
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Check: Uphill distance: miles. Downhill distance: miles. The distances are equal.
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Finding Uphill and Downhill Hiking Speeds Using Equal Distances
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