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?
0.03 * 3.15 = 0.095
3.26 - 3.15 = 0.11
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?
how do you set this problem up
To determine if the train company will live up to its reputation on this trip, we need to calculate the range of acceptable times based on the given 3% error margin.
Step 1: Calculate the lower limit of the acceptable time:
3.15 hours * (1 - 0.03) = 3.15 * 0.97 = 3.0555 hours
Step 2: Calculate the upper limit of the acceptable time:
3.15 hours * (1 + 0.03) = 3.15 * 1.03 = 3.2445 hours
Step 3: Compare the actual time of 3.26 hours to the acceptable time range:
3.0555 hours ≤ 3.26 hours ≤ 3.2445 hours
Since the actual time of 3.26 hours falls outside the acceptable range of 3.0555 to 3.2445 hours, the train company will not live up to its reputation on this trip.
To determine if the train company lives up to its reputation, we need to calculate the acceptable error margin based on the expected trip time.
First, let's calculate the acceptable error range. The train company allows a 3% error on the expected time, which can be calculated as follows:
3% of the expected time = 0.03 * 3.15 hours = 0.0945 hours
Now, let's determine the acceptable range within which the train's actual arrival time should fall.
Lower bound: Expected time - Acceptable error
Upper bound: Expected time + Acceptable error
Lower bound: 3.15 hours - 0.0945 hours = 3.0555 hours
Upper bound: 3.15 hours + 0.0945 hours = 3.2445 hours
Since the train arrived in 3.26 hours, which is beyond the upper bound of 3.2445 hours, the actual arrival time falls outside the acceptable error range.
Therefore, the train company did not live up to its reputation on this trip, as the train arrived outside the allowed error margin of 3%.