Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 236 miles in the same time that Dana travels 224 miles. If Chuck’s rate of travel is 3 mph more than Dana’s, and they travel the same length of time, at what speed does Chuck travel?
To solve this problem, we'll use the formula: Speed = Distance/Time.
Let's assume Dana's speed is x mph. Since Chuck's speed is 3 mph more than Dana's, Chuck's speed is (x + 3) mph.
We know that the time they both travel is the same.
Dana's time = Distance/Speed = 224/x
Chuck's time = Distance/Speed = 236/(x + 3)
Since their times are equal:
224/x = 236/(x + 3)
To solve this equation, we'll cross-multiply and solve for x:
224(x + 3) = 236x
224x + 672 = 236x
672 = 236x - 224x
672 = 12x
Dividing both sides by 12:
x = 672/12
x = 56
So, Dana's speed is 56 mph.
And since Chuck's speed is 3 mph more than Dana, Chuck's speed is 56 + 3 = 59 mph.
Therefore, Chuck travels at a speed of 59 mph.