Question

jean climbed 2/3 of the distance to the top of the cliff shown on the number line. terry climbed 1/3 of the distance less than jean. steve climbed 1/5 of the distance more than jean

Answer 1

Let's break down the problem step by step.

1. **Jean's Climb:**
- Jean climbed \( \frac{2}{3} \) of the distance to the top of the cliff. We can represent the total distance to the top of the cliff as \( d \), therefore Jean climbed:
\[
J = \frac{2}{3}d
\]

2. **Terry's Climb:**
- Terry climbed \( \frac{1}{3} \) of the distance less than Jean. This means Terry climbed:
\[
T = J - \frac{1}{3} = \frac{2}{3}d - \frac{1}{3}
\]
- To combine the terms, we first express \( \frac{1}{3} \) with a common denominator of 3. So, we get:
\[
T = \frac{2}{3}d - \frac{1}{3} = \frac{2d - 1}{3}
\]

3. **Steve's Climb:**
- Steve climbed \( \frac{1}{5} \) of the distance more than Jean. So, Steve climbed:
\[
S = J + \frac{1}{5} = \frac{2}{3}d + \frac{1}{5}
\]
- To combine these fractions, we will also need a common denominator. The least common multiple of 3 and 5 is 15:
\[
S = \frac{10}{15}d + \frac{3}{15} = \frac{10d + 3}{15}
\]

Now we have the expressions for the distances climbed by Jean, Terry, and Steve:
- Jean: \( J = \frac{2}{3}d \)
- Terry: \( T = \frac{2d - 1}{3} \)
- Steve: \( S = \frac{10d + 3}{15} \)

You can substitute a specific value for \( d \) to evaluate their distances further if necessary.