# Please help with the following word problem.Katy travels 180 miles in the same time Joe travels 120 miles. If Katy’s speed is 20 mph faster than Joe’s speed, find Katy’s speed and Joe’s...

Please help with the following word problem.

Katy travels 180 miles in the same time Joe travels 120 miles. If Katy’s speed is 20 mph faster than Joe’s speed, find Katy’s speed and Joe’s speed. Include units in your answer.

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### 1 Answer

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.**