Jon and Melissa agree to meet in Chicago for the weekend. Jon travels 236 miles in the same time that Melissa travels 224 miles. If Jons rate of travel is 3 mph more than Melissas, and they travel the same length of time, at what speed does Jon travel?
To solve this problem, let's start by setting up equations to represent the given information.
Let's assume Melissa's speed as "x" mph. Since Jon's speed is 3 mph more than Melissa's, Jon's speed can be represented as "x + 3" mph.
The formula to calculate the time it takes to travel a certain distance is:
Time = Distance / Speed
According to the problem, Jon travels 236 miles in the same time Melissa travels 224 miles. So we can set up an equation as follows:
236 / (x + 3) = 224 / x
To solve this equation, we can cross-multiply:
236x = 224(x + 3)
Now, let's distribute and simplify:
236x = 224x + 672
Next, let's move all the variables to one side by subtracting 224x from both sides:
12x = 672
Finally, we can solve for x by dividing both sides by 12:
x = 672 / 12
x = 56
So, Melissa's speed is 56 mph. Since Jon's speed is 3 mph more than Melissa's, Jon's speed is:
56 + 3 = 59 mph
Therefore, Jon travels at a speed of 59 mph.