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Hugo lives in the northwest corner of Greene County, Lena lives miles away in the southeast corner, and the office where they work is directly between them. On Monday, Hugo took the bus into work, taking a direct route at miles per hour. Lena left at the same time, taking her car along a direct route at a speed of miles per hour. The two coworkers arrive at the office at the same time. How long did the commute take? If necessary, round your answer to the nearest minute. hours and minutes
Full solution
Q. Hugo lives in the northwest corner of Greene County, Lena lives miles away in the southeast corner, and the office where they work is directly between them. On Monday, Hugo took the bus into work, taking a direct route at miles per hour. Lena left at the same time, taking her car along a direct route at a speed of miles per hour. The two coworkers arrive at the office at the same time. How long did the commute take? If necessary, round your answer to the nearest minute. hours and minutes
- Define Question Prompt: First, let's define the question prompt clearly: ＂How long did the commute take for Hugo and Lena to reach the office, given their respective speeds and the fact that they started at the same time and arrived together?＂
- Calculate Distance: We know that Hugo and Lena live miles apart and the office is directly between them. This means that the distance each of them has to travel to get to the office is half of miles.Distance for each = miles = miles
- Calculate Hugo's Time: Hugo's speed is miles per hour, and Lena's speed is miles per hour. Since they both arrive at the same time, we can use the formula to find the time it took for each of them to travel to the office.
- Calculate Hugo's Time: Let's calculate the time it took for Hugo to reach the office:Time for Hugo = Distance / Speed = miles / miles per hour
- Calculate Lena's Time: Performing the calculation for Hugo's travel time:Time for Hugo = hours
- Identify Math Error: Now, let's calculate the time it took for Lena to reach the office using the same formula:Time for Lena = Distance / Speed = miles / miles per hour
- Identify Math Error: Now, let's calculate the time it took for Lena to reach the office using the same formula:Time for Lena = Distance / Speed = miles / miles per hourPerforming the calculation for Lena's travel time:Time for Lena = hours
- Identify Math Error: Now, let's calculate the time it took for Lena to reach the office using the same formula:Time for Lena = Distance / Speed = miles / miles per hourPerforming the calculation for Lena's travel time:Time for Lena = hoursSince Hugo and Lena arrive at the same time, we should expect their travel times to be the same. However, we have two different times. This indicates a math error in our calculations.
