# Help me solve the following word problem.Katy travels 140 miles in the same time Joe travels 80 miles. If Katy’s speed is 10 mph faster than Joe’s speed, find Katy’s speed and Joe’s...

Help me solve the following word problem.

Katy travels 140 miles in the same time Joe travels 80 miles. If Katy’s speed is 10 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 need to use the distance equation such that:

`d = s*t ` (s represents the speed, t represents the time and d the distance)

You need to notice that the problem provides the information that Joe and Katy travel the specified distances in the same time, hence, you may write the following relation such that:

`140/s_1 = 80/s_2`

Notice that you may write the Katy's speed in terms of Joe's speed, since Katy is 10 mph faster than Joe such that:

`140/(s_2+10) = 80/s_2`

Performing the cross multiplication yields:

`80s_2 + 800 = 140s_2 => 140s_2 - 80s_2 = 800`

`60s_2 = 800 => s_2 = 80/6 ~~ 13.3 mph`

Since the Joe's speed is of `13.3` mph, hence, the Katy's speed is of `13.3+10 = 23.3 ` mph.

**Hence, evaluating the Joe's speed yields 13.3 mph and evaluating Katy's speed yields 23.3 mph.**