Question

Manuel traveled 7 hours nonstop to Mexico, a total of 200 miles. He took a train part of the way, which averaged 40 mph, and then took a bus the remaining distance, which averaged 30 mph. How long was Manuel on the train?

A. 2 hours
B. 2.5 hours
C. 3 hours
D. 3.5 hours

Answer 1

The given problem can be solved by setting up a system of equations using Manuel's travel times and the speeds of the train and the bus. However, the calculation provided resulted in a negative time, indicating an error in the approach, so a different calculation should be used to find the correct time Manuel was on the train.

Step-by-step explanation:

To determine how long Manuel was on the train, we can use the information given about his total travel time and the speeds of the train and bus to set up a system of equations. Let's denote the time Manuel was on the train as T and the time on the bus as B. We know that the sum of T and B is the total travel time, which is 7 hours. We also know that the train traveled at an average speed of 40 mph, while the bus traveled at an average speed of 30 mph, and the total distance traveled was 200 miles.

The system of equations is as follows:

• T + B = 7
• 40T + 30B = 200

We can solve for T using substitution or elimination methods. For example, we can express B as 7 - T from the first equation and substitute it into the second equation:

40T + 30(7 - T) = 200

40T + 210 - 30T = 200

10T = 200 - 210

10T = -10

T = -1

In this case, the negative result indicates that there is likely an error in the calculations since we cannot have negative time. Hence, we may need to recheck our equations or look for a different approach.