Let's break down the problem step by step.
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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: \[ J = \frac{2}{3}d \]
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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: \[ T = \frac{2}{3}d - \frac{1}{3} = \frac{2d - 1}{3} \]
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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.
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