Final answer:
By calculating the speeds of Hansel (2.8 m/s) and Gretel (2.4286 m/s) and their respective times to reach the bottom of the 2400m mountain, we determine that Hansel will reach the bottom first in approximately 14 minutes and 17 seconds, matching closest to option (a).
Step-by-step explanation:
The student wants to know who will reach the bottom of the mountain first, Hansel, who is skiing at a rate of 14m every 5 seconds, or Gretel, who is snowboarding at a rate of 17m every 7 seconds, considering it is 2400m to the bottom.
First, we calculate their speeds in meters per second (m/s) by dividing the distance they cover by the time it takes:
- Hansel's speed: 14m / 5s = 2.8 m/s.
- Gretel's speed: 17m / 7s = 2.4286 m/s.
Next, we find the time it takes for each to reach the bottom by dividing the total distance (2400m) by their speeds:
- Hansel's time: 2400m / 2.8 m/s = 857.14 seconds (or 14 minutes and 17 seconds).
- Gretel's time: 2400m / 2.4286 m/s = 988.235 seconds (or 16 minutes and 28 seconds).
Therefore, Hansel will reach the bottom first. Converting Hansel's time to minutes:
- 857.14 seconds = 857.14 s × (1 minute/60 seconds) ≈ 14.29 minutes.
The closest answer provided is option (a), stating that Hansel will reach the bottom first in 15 minutes, which we can interpret as approximately 15 minutes.
The correct answer is option (a): Hansel will reach the bottom first in 15 minutes.