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

1 answer

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.