Example: Finding Uphill and Downhill Hiking Speeds
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 minutes to hike uphill from the parking lot to the lookout tower. It takes her minutes to hike back down to the parking lot. Her speed going downhill is miles per hour faster than her speed going uphill. Find Suzy's uphill and downhill speeds.
- Read and draw: Sketch the route. The uphill distance ( minutes) and downhill distance ( minutes, mph faster) are equal. Create a rate–time–distance table.
- 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: minutes hour, and minutes hour. Multiply rate by time to find the distance expressions:
| Rate (mph) | Time (hrs) | Distance (miles) | |
|---|---|---|---|
| Uphill | |||
| Downhill |
- Translate: The uphill distance and downhill distance are exactly the same:
- Solve: Clear the fractions by multiplying both sides by the LCD, which is :
Subtract from both sides: . Divide by : . The uphill speed is mph. The downhill speed is mph.
-
Check: Uphill: miles. Downhill: miles. Both equal miles.
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Answer: Suzy's uphill speed is mph and her downhill speed is mph.
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Example: Finding Uphill and Downhill Hiking Speeds
Example: Finding Upstream and Downstream Boat Speeds