Emily takes a trip, driving with a constant velocity of 79.5 km/h to the north except for a 22 min rest stop. If Emily's average velocity is 68.8 km/h to the north, how long does the trip take?
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To find the total time of the trip, we need to consider the time spent driving and the time spent during the rest stop.
Let's start by finding the time spent driving. We can use the formula:
Time = Distance / Velocity
The distance traveled during the driving portion of the trip is equal to the total distance minus the distance covered during the rest stop. Since the rest stop has a duration of 22 minutes, we need to convert it into hours by dividing it by 60.
Rest stop time = 22 minutes / 60 minutes/hour = 0.367 hours
Next, we'll find the distance covered during the rest stop by multiplying the rest stop time by the velocity during the rest stop, which is 0 km/h.
Distance during rest stop = Rest stop time * Velocity during rest stop = 0.367 hours * 0 km/h = 0 km
Now, let's calculate the distance covered during the driving portion of the trip. We can use the formula:
Distance = Velocity * Time
We know the average velocity during the driving portion is 68.8 km/h and we want to find the time spent driving, so we rearrange the formula to solve for time:
Time = Distance / Velocity
Time driving = (Total distance - Distance during rest stop) / Velocity
The total distance of the trip is the same as the distance covered during the driving portion, so we can simplify the equation:
Time driving = (Total distance - 0 km) / 68.8 km/h
To find the total distance, we can use the formula:
Distance = Velocity * Time
Total distance = 79.5 km/h * Time driving + 0 km * Rest stop time
We can substitute this into the previous equation:
Time driving = (79.5 km/h * Time driving + 0 km * 0.367 hours) / 68.8 km/h
Now we can solve for Time driving:
Time driving = (79.5 km/h * Time driving) / 68.8 km/h
Rearranging the equation:
Time driving * 68.8 km/h = 79.5 km/h * Time driving
Simplifying:
Time driving * 68.8 km/h - Time driving * 79.5 km/h = 0
Factoring out Time driving:
Time driving * (68.8 km/h - 79.5 km/h) = 0
Since the equation equals zero, this means that either Time driving or (68.8 km/h - 79.5 km/h) is equal to zero. However, a negative time doesn't make sense in this context, so we can disregard it. Therefore, the time spent driving can be zero:
Time driving = 0
However, this scenario doesn't make sense because it implies Emily didn't drive at all. Therefore, there must be an error in the information provided or the question itself.