A locomotive train is on its way from Chicago, IL to Madison, WI. The trip is said to last 3.15 hours. When the train arrives in Madison the conductor notices it actually took them 3.26 hours. The train company prides itself on always having its trains to the station within a 3% error of the expected time. Will the train company live up to its reputation on this trip?
the difference is .11 hours
.11/3.15 = 0.0349 ≈ 3.5%
To determine if the train company lived up to its reputation on this trip, we need to calculate the acceptable error range based on a 3% deviation from the expected time.
First, we calculate the acceptable error range:
3% of 3.15 hours = 0.03 * 3.15 = 0.0945 hours
Next, we convert this into minutes to make it easier for comparison purposes:
0.0945 hours * 60 minutes/hour = 5.67 minutes
Therefore, the acceptable error range is 5.67 minutes.
Now let's compare the actual time taken (3.26 hours) with the expected time (3.15 hours) to determine if it falls within the acceptable range:
Actual time taken - Expected time = 3.26 hours - 3.15 hours = 0.11 hours
Now, convert this into minutes:
0.11 hours * 60 minutes/hour = 6.6 minutes
Since 6.6 minutes is greater than the acceptable error range of 5.67 minutes, we can conclude that the train company did not live up to its reputation on this trip as it exceeded the allowable deviation by 6.6 minutes.
To determine if the train company lived up to its reputation on this trip, we can calculate the allowed error for a 3% deviation from the expected time.
First, we need to find 3% of the expected time:
3% of 3.15 hours = 0.03 * 3.15 = 0.0945 hours
Next, we convert this deviation to minutes:
0.0945 hours * 60 minutes/hour = 5.67 minutes
Therefore, the train company's allowed deviation for this trip is approximately 5.67 minutes.
Now, we compare the actual arrival time (3.26 hours) with the expected time (3.15 hours).
To do this, we need to calculate the difference in minutes between the two times:
3.26 hours * 60 minutes/hour = 195.6 minutes
3.15 hours * 60 minutes/hour = 189 minutes
The actual arrival time was 195.6 minutes, and the expected arrival time was 189 minutes. The difference between the two is:
195.6 minutes - 189 minutes = 6.6 minutes
Since the actual deviation (6.6 minutes) is greater than the allowed deviation (5.67 minutes), the train company did not live up to its reputation on this trip.