Question

Rumi and Noam are learning to rock climb.Rumi starts at the bottom and climbs 10ft each minute non starts 10 ft of an climbs 8ft each minute

Answer 1

Let's clarify the climbing scenario involving Rumi and Noam:

- **Rumi** starts at the bottom and climbs **10 feet per minute**.
- **Noam** starts **10 feet up** and climbs **8 feet per minute**.

Now, let's analyze how their positions change over time.

### Rumi's Position
Rumi starts at the bottom (0 ft) and climbs at a rate of 10 feet per minute. After \( t \) minutes, Rumi's height can be expressed as:
\[
R(t) = 10t \text{ feet}
\]

### Noam's Position
Noam starts 10 feet up (10 ft) and climbs at a rate of 8 feet per minute. After \( t \) minutes, Noam's height can be expressed as:
\[
N(t) = 10 + 8t \text{ feet}
\]

### Finding when Rumi catches up to Noam
To find out when Rumi catches up to Noam, we set their height equations equal to each other:
\[
10t = 10 + 8t
\]

Now, let's solve for \( t \):
1. Subtract \( 8t \) from both sides:
\[
10t - 8t = 10
\]
\[
2t = 10
\]

2. Divide both sides by 2:
\[
t = 5
\]

### Conclusion
After 5 minutes, Rumi will catch up to Noam. We can calculate their height at that time:

- Rumi's height:
\[
R(5) = 10 \times 5 = 50 \text{ feet}
\]

- Noam's height:
\[
N(5) = 10 + 8 \times 5 = 10 + 40 = 50 \text{ feet}
\]

Thus, both Rumi and Noam will be at **50 feet** after **5 minutes**.