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?
how did u get that??
2.72 hours
To find the time it takes for the trip, we can use the formula:
Time = Distance / Velocity
Let's break down the trip into two parts: the time taken while driving and the time taken during the rest stop.
1. The time taken while driving:
During this time, Emily maintains a constant velocity of 79.5 km/h to the north. Let's assume the driving time is represented by t hours.
Since the average velocity is given by 68.8 km/h, we can set up the equation:
Distance driven = Average velocity * Time taken while driving
Distance driven = 68.8 km/h * t
2. The time taken during the rest stop:
Emily takes a 22-minute rest stop, which needs to be converted to hours. Since 1 hour is equivalent to 60 minutes, the rest stop time in hours is 22 minutes / 60 minutes.
Now, to calculate the total time taken for the trip, we need to add the driving time and the rest stop time:
Total time = Time taken while driving + Time taken during the rest stop
Total time = t hours + (22 minutes / 60 minutes) hours
Since we already know the average velocity and average velocity is the total distance divided by the total time taken, we can set up the equation:
Average velocity = Total distance / Total time
Plugging in the values:
68.8 km/h = (Distance driven) / (Total time)
Now, we need to solve for the driving distance. Since distance is calculated as velocity multiplied by time:
Distance driven = 79.5 km/h * t
Substituting this in the equation:
68.8 km/h = (79.5 km/h * t) / (t hours + (22 minutes / 60 minutes) hours)
Now, we can solve for t, the time taken while driving:
68.8 km/h = (79.5 km/h * t) / (t + (22/60) hours)
To solve this equation, we can cross-multiply:
68.8 km/h * (t + (22/60) hours) = 79.5 km/h * t
Simplifying:
68.8t + 68.8(22/60) = 79.5t
Now, we can isolate t on one side of the equation:
68.8t - 79.5t = 68.8(22/60)
Simplifying:
-10.7t = 68.8(22/60)
Dividing both sides by -10.7:
t = (68.8(22/60)) / -10.7
Now, by evaluating this expression, we can find the value of t, which represents the time taken for driving.
Finally, to find the total time taken for the trip, you would add the time taken for driving (t) and the rest stop time (22 minutes / 60 minutes).