Problem

When Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train travels an average of 48 miles per hour faster than his driving. Assume that the train travels the same distance as the car.

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The distance Fritz travels to work is \(\boxed{36}\) miles.

Steps

Step 1 :Let's denote the distance Fritz travels to work as \(d\), Fritz's driving speed as \(s\), the time Fritz drives to work as \(t1\), and the time Fritz takes the train to work as \(t2\).

Step 2 :We can set up two equations based on the given information: \(d = s * t1\) and \(d = (s + 48) * t2\).

Step 3 :We know that \(t1 = 36\) minutes which is \(0.6\) hours and \(t2 = 20\) minutes which is \(1/3\) hours. We can substitute these values into the equations.

Step 4 :Substituting the values of \(t1\) and \(t2\) into the equations, we get: \(d = 0.6s\) and \(d = 0.333333333333333*s + 16.0\).

Step 5 :Solving these equations, we find that the distance \(d\) Fritz travels to work is \(36\) miles and his driving speed \(s\) is \(60\) miles per hour.

Step 6 :Final Answer: The distance Fritz travels to work is \(\boxed{36}\) miles.

link_gpt