Question: Question 5
It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours.
Assume the pack ice was drifting at a constant rate, and that Todd’s snowmobile was traveling at a constant speed relative to the pack ice.
What was the speed of Todd's snowmobile?
20 miles per hour
26 miles per hour
10 miles per hour
4 miles per hour
1. **State the problem:** Todd travels 330 miles over pack ice in 11 hours one way and 330 miles in 15 hours on the return. The pack ice drifts at a constant speed, and Todd's snowmobile speed relative to the ice is constant. We need to find the snowmobile's speed relative to the ice.
2. **Define variables:**
- Let $s$ = speed of the snowmobile relative to the ice (in miles per hour).
- Let $d$ = speed of the drifting pack ice (in miles per hour).
3. **Write equations for each trip:**
- Going with the drift: effective speed = $s + d$, time = 11 hours, distance = 330 miles.
$$330 = (s + d) \times 11$$
- Returning against the drift: effective speed = $s - d$, time = 15 hours, distance = 330 miles.
$$330 = (s - d) \times 15$$
4. **Express equations:**
$$s + d = \frac{330}{11} = 30$$
$$s - d = \frac{330}{15} = 22$$
5. **Add the two equations to eliminate $d$:**
$$ (s + d) + (s - d) = 30 + 22$$
$$ 2s = 52$$
$$ s = \frac{52}{2} = 26$$
6. **Interpretation:** The speed of the snowmobile relative to the ice is $\boxed{26}$ miles per hour.
7. **Check:**
- Calculate $d$:
$$ s + d = 30 \Rightarrow 26 + d = 30 \Rightarrow d = 4$$
- Check return speed:
$$ s - d = 26 - 4 = 22$$ matches the earlier calculation.
**Final answer:** Todd's snowmobile speed relative to the pack ice is **26 miles per hour**.