The distance from Lubbock to Dallas is 346 miles or 557 km. If my family leaves at 10:00 A.M. and travels at a constant 70 mph, what is our estimated time of arrival? Show your work and include formula (s) and units.
The correct answer and explanation is:
To calculate the estimated time of arrival, we first need to determine how long it will take to travel from Lubbock to Dallas. We know the distance and the speed, so we can use the formula: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}
Step 1: Convert units if necessary
- The distance from Lubbock to Dallas is given as 346 miles.
- The speed is 70 miles per hour (mph), which is the speed at which the family will be traveling.
Step 2: Calculate time
Now, plug the values into the formula: Time=346 miles70 mph=4.942857 hours\text{Time} = \frac{346 \, \text{miles}}{70 \, \text{mph}} = 4.942857 \, \text{hours}
So, it will take approximately 4.94 hours to drive from Lubbock to Dallas.
Step 3: Convert hours to hours and minutes
Next, convert the decimal part (0.94 hours) into minutes: 0.94 hours×60 minutes per hour=56.4 minutes0.94 \, \text{hours} \times 60 \, \text{minutes per hour} = 56.4 \, \text{minutes}
So, the travel time is approximately 4 hours and 56 minutes.
Step 4: Estimate time of arrival
If the family leaves at 10:00 A.M., you would add the travel time of 4 hours and 56 minutes: 10:00 A.M.+4 hours and 56 minutes=2:56 P.M.10:00 \, \text{A.M.} + 4 \, \text{hours and} \, 56 \, \text{minutes} = 2:56 \, \text{P.M.}
Final Answer:
The estimated time of arrival in Dallas is 2:56 P.M..
This approach assumes that there are no delays due to traffic, stops, or other factors, and the family is able to maintain a constant speed of 70 mph.