You should remember the equation that relates the distance, speed and time such that:

`d = s*t => t = d/s`

d represents the distance, s represents the speed and t represets the time.

The problem provides the distances travelled by Katy and Joe in the same time such that:

`t = 180/s_1 = 120/s_2`

`s_1` represents the Katy's speed and `s_2 ` represents Joe's speed

Notice that the problem provides a relation between the Joe's speed nd Katy's speed such that:

`s_1= s_2 + 20`

`180/(s_2 + 20) = 120/s_2 => 120(s_2 + 20) = 180s_2`

`120s_2 + 2400 = 180s_2 => 2400 = 180s_2 - 120s_2`

`60s_2=2400 => s_2 = 240/6 => s_2 = 40 mph`

Since `s_2` represents the Joe's speed, you may find Katy's speed such that:

`s_1 = s_2 + 20 => s_1 = 40+20 = 60 mph`

**Hence, evaluating the Joe's speed and Katy's speed yields 40 mph and 60 mph.**

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