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Hiking Time worksheet

Grade 6 · CCSS 6.RP.A.3.b, 6.RP.A.3.d

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Method: Naismith + Langmuir descent
- Trail distance: 12 km
- Total elevation gain: 850 m
- Gentle descent (5°–12° slopes): 350
- Steep descent (over 12°): 380
- Walking speed on the flat: 5 km/h
- Climbing allowance: height gained per extra hour: 450 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
2.
Problem 2.
- Method: Naismith + Langmuir descent
- Trail distance: 11 km
- Total elevation gain: 850 m
- Gentle descent (5°–12° slopes): 350
- Steep descent (over 12°): 400
- Walking speed on the flat: 5 km/h
- Climbing allowance: height gained per extra hour: 500 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
3.
Problem 3.
- Method: Naismith's rule
- Trail distance: 15 km
- Total elevation gain: 1,100 m
- Walking speed on the flat: 7 km/h
- Climbing allowance: height gained per extra hour: 550 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
4.
Problem 4.
- Method: Naismith + Langmuir descent
- Trail distance: 13 km
- Total elevation gain: 975 m
- Gentle descent (5°–12° slopes): 240
- Steep descent (over 12°): 540
- Walking speed on the flat: 6 km/h
- Climbing allowance: height gained per extra hour: 600 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
5.
Problem 5.
- Method: Naismith + Langmuir descent
- Trail distance: 10 km
- Total elevation gain: 700 m
- Gentle descent (5°–12° slopes): 260
- Steep descent (over 12°): 600
- Walking speed on the flat: 4 km/h
- Climbing allowance: height gained per extra hour: 750 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
6.
Problem 6.
- Method: Naismith's rule
- Trail distance: 14 km
- Total elevation gain: 525 m
- Walking speed on the flat: 5 km/h
- Climbing allowance: height gained per extra hour: 800 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
7.
Problem 7.
- Method: Naismith's rule
- Trail distance: 10 km
- Total elevation gain: 1,000 m
- Walking speed on the flat: 4 km/h
- Climbing allowance: height gained per extra hour: 550 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
8.
Problem 8.
- Method: Naismith + Langmuir descent
- Trail distance: 13 km
- Total elevation gain: 800 m
- Gentle descent (5°–12° slopes): 250
- Steep descent (over 12°): 375
- Walking speed on the flat: 5 km/h
- Climbing allowance: height gained per extra hour: 600 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
9.
Problem 9.
- Method: Naismith + Langmuir descent
- Trail distance: 10 km
- Total elevation gain: 850 m
- Gentle descent (5°–12° slopes): 310
- Steep descent (over 12°): 400
- Walking speed on the flat: 5 km/h
- Climbing allowance: height gained per extra hour: 700 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer
10.
Problem 10.
- Method: Naismith's rule
- Trail distance: 12 km
- Total elevation gain: 700 m
- Walking speed on the flat: 5 km/h
- Climbing allowance: height gained per extra hour: 500 m per hour
- Pace adjustment: 0%
- Breaks: 0 min
Find: Estimated hiking time
Answer

Answer key: Hiking Time worksheet

1. Estimated hiking time: 4 h 18 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{12 km}{5 km/h} \times 60$ $= 144 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{850 m}{450 m/h} \times 60$ $= 113.3333 min$
3. Langmuir's downhill correction: take off 10 min per 300 m of gentle slope, add 10 min per 300 m of steep slope
  $\frac{(380 m - 350 m)}{300 m} \times 10$ $= 1 min$
4. Add them up to get your moving time: distance time plus climbing time plus the downhill correction
  $144 + 113.3333 + 1$ $= 258.3333 min$
5. Add the breaks, then write the minutes as hours and minutes
  $258.3333 + 0$ $= 258.33 min$ $= 4 h 18 min$
2. Estimated hiking time: 3 h 56 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{11 km}{5 km/h} \times 60$ $= 132 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{850 m}{500 m/h} \times 60$ $= 102 min$
3. Langmuir's downhill correction: take off 10 min per 300 m of gentle slope, add 10 min per 300 m of steep slope
  $\frac{(400 m - 350 m)}{300 m} \times 10$ $= 1.6667 min$
4. Add them up to get your moving time: distance time plus climbing time plus the downhill correction
  $132 + 102 + 1.6667$ $= 235.6667 min$
5. Add the breaks, then write the minutes as hours and minutes
  $235.6667 + 0$ $= 235.67 min$ $= 3 h 56 min$
3. Estimated hiking time: 4 h 09 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{15 km}{7 km/h} \times 60$ $= 128.5714 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{1,100 m}{550 m/h} \times 60$ $= 120 min$
3. Add them up to get your moving time: distance time plus climbing time
  $128.5714 + 120$ $= 248.5714 min$
4. Add the breaks, then write the minutes as hours and minutes
  $248.5714 + 0$ $= 248.57 min$ $= 4 h 09 min$
4. Estimated hiking time: 3 h 58 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{13 km}{6 km/h} \times 60$ $= 130 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{975 m}{600 m/h} \times 60$ $= 97.5 min$
3. Langmuir's downhill correction: take off 10 min per 300 m of gentle slope, add 10 min per 300 m of steep slope
  $\frac{(540 m - 240 m)}{300 m} \times 10$ $= 10 min$
4. Add them up to get your moving time: distance time plus climbing time plus the downhill correction
  $130 + 97.5 + 10$ $= 237.5 min$
5. Add the breaks, then write the minutes as hours and minutes
  $237.5 + 0$ $= 237.5 min$ $= 3 h 58 min$
5. Estimated hiking time: 3 h 37 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{10 km}{4 km/h} \times 60$ $= 150 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{700 m}{750 m/h} \times 60$ $= 56 min$
3. Langmuir's downhill correction: take off 10 min per 300 m of gentle slope, add 10 min per 300 m of steep slope
  $\frac{(600 m - 260 m)}{300 m} \times 10$ $= 11.3333 min$
4. Add them up to get your moving time: distance time plus climbing time plus the downhill correction
  $150 + 56 + 11.3333$ $= 217.3333 min$
5. Add the breaks, then write the minutes as hours and minutes
  $217.3333 + 0$ $= 217.33 min$ $= 3 h 37 min$
6. Estimated hiking time: 3 h 27 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{14 km}{5 km/h} \times 60$ $= 168 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{525 m}{800 m/h} \times 60$ $= 39.375 min$
3. Add them up to get your moving time: distance time plus climbing time
  $168 + 39.375$ $= 207.375 min$
4. Add the breaks, then write the minutes as hours and minutes
  $207.375 + 0$ $= 207.38 min$ $= 3 h 27 min$
7. Estimated hiking time: 4 h 19 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{10 km}{4 km/h} \times 60$ $= 150 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{1,000 m}{550 m/h} \times 60$ $= 109.0909 min$
3. Add them up to get your moving time: distance time plus climbing time
  $150 + 109.0909$ $= 259.0909 min$
4. Add the breaks, then write the minutes as hours and minutes
  $259.0909 + 0$ $= 259.09 min$ $= 4 h 19 min$
8. Estimated hiking time: 4 h 00 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{13 km}{5 km/h} \times 60$ $= 156 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{800 m}{600 m/h} \times 60$ $= 80 min$
3. Langmuir's downhill correction: take off 10 min per 300 m of gentle slope, add 10 min per 300 m of steep slope
  $\frac{(375 m - 250 m)}{300 m} \times 10$ $= 4.1667 min$
4. Add them up to get your moving time: distance time plus climbing time plus the downhill correction
  $156 + 80 + 4.1667$ $= 240.1667 min$
5. Add the breaks, then write the minutes as hours and minutes
  $240.1667 + 0$ $= 240.17 min$ $= 4 h 00 min$
9. Estimated hiking time: 3 h 16 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{10 km}{5 km/h} \times 60$ $= 120 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{850 m}{700 m/h} \times 60$ $= 72.8571 min$
3. Langmuir's downhill correction: take off 10 min per 300 m of gentle slope, add 10 min per 300 m of steep slope
  $\frac{(400 m - 310 m)}{300 m} \times 10$ $= 3 min$
4. Add them up to get your moving time: distance time plus climbing time plus the downhill correction
  $120 + 72.8571 + 3$ $= 195.8571 min$
5. Add the breaks, then write the minutes as hours and minutes
  $195.8571 + 0$ $= 195.86 min$ $= 3 h 16 min$
10. Estimated hiking time: 3 h 48 min
1. Time for the distance: divide it by your walking speed, then times 60 for minutes
  $\frac{12 km}{5 km/h} \times 60$ $= 144 min$
2. Time for climbing: divide the total climb by the height you gain per hour, then times 60
  $\frac{700 m}{500 m/h} \times 60$ $= 84 min$
3. Add them up to get your moving time: distance time plus climbing time
  $144 + 84$ $= 228 min$
4. Add the breaks, then write the minutes as hours and minutes
  $228 + 0$ $= 228 min$ $= 3 h 48 min$