Emily takes a trip, driving with a constant velocity of 89.5 km/h to the north except for a 22 min rest stop. If Emily's average velocity is 70.8 km/h to the north, how long does the trip take?
Let t be the total time the trip takes in hours. We can form an equation from the statement: (89.5*(t-22/60))/(t)=70.8
First, we need to solve for t:
89.5*t - 89.5*(22/60) = 70.8*t
89.5*t - 33.07 = 70.8*t
18.7*t = 33.07
t = 1.77 hours
Now, we need to convert 1.77 hours into hours and minutes:
1 hour + 0.77 hours * (60 minutes / 1 hour) = 1 hour 46 minutes
The trip takes 1 hour 46 minutes.
To determine the total time of Emily's trip, we need to take into account both her driving time and the duration of her rest stop.
First, let's calculate the driving time. We know that Emily's average velocity during the driving portion of the trip is 70.8 km/h to the north. The distance she travels can be found using the formula:
Distance = Velocity × Time
Since the velocity is given in km/h, the distance will also be in kilometers. Let's denote the driving time as "t" (in hours), then we have:
Distance = 70.8 km/h × t
Next, we consider the rest stop, which lasts for 22 minutes. To include this in our calculations, we need to convert the rest stop duration to hours. There are 60 minutes in an hour, so 22 minutes is equal to:
Rest stop duration = 22 minutes ÷ 60 minutes/hour
Since the rest stop duration is given in hours, we can denote it as "r".
Now, to find the total time of the trip, we add the driving time and the rest stop duration:
Total time = driving time + rest stop duration
Total time = t + r
Since we know the average velocity and the velocity during the driving portion of the trip, we can set up the equation:
70.8 km/h = (Distance driven)/(Total time)
Substituting the formula for distance and rearranging the equation, we have:
70.8 km/h = (70.8 km/h × t)/(t + r)
Now we can solve for t:
70.8 km/h × (t + r) = 70.8 km/h × t
70.8 km/h × t + 70.8 km/h × r = 70.8 km/h × t
70.8 km/h × r = 0
Since the left-hand side of the equation is zero, we can conclude that r = 0, meaning that the rest stop duration does not affect the average velocity. Therefore, the total time of Emily's trip is equal to the driving time, which is given as:
Total time = t
In order to find t, we need more information.