A person takes a trip, driving with a constant speed of 92.0 km/h except for a 22.0 min rest stop. If the person's average speed is 78.6 km/h, how long is the trip?
What’s the right answer then Carey.
What’s the correct answer
To find the length of the trip, we need to use the formula:
Total time = Time spent driving + Time spent resting
Given that the person drives at a constant speed of 92.0 km/h, we can calculate the time spent driving by dividing the distance by the speed:
Time spent driving = Distance / Speed
The distance is not given directly, but we can calculate it by multiplying the average speed by the total time:
Distance = Average speed × Total time
So, the equation can be rewritten as:
Time spent driving = (Average speed × Total time) / Speed
Now, let's calculate the time spent driving:
Time spent driving = (78.6 × Total time) / 92.0
The time spent resting is given as 22.0 minutes.
Now, we can write the equation for the total time:
Total time = Time spent driving + Time spent resting
Since the average speed is defined as the total distance divided by the total time, we can also express the total distance in terms of the average speed and the total time:
Total distance = Average speed × Total time
Now, let's substitute the equations for the time spent driving and the total distance into the total time equation:
Total time = (78.6 × Total time) / 92.0 + 22.0
To solve for the total time, we can multiply both sides by 92.0 to eliminate the fraction:
92.0 × Total time = 78.6 × Total time + 2034.4
Now, subtract 78.6 × Total time from both sides:
92.0 × Total time - 78.6 × Total time = 2034.4
13.4 × Total time = 2034.4
Divide both sides by 13.4 to solve for Total time:
Total time = 2034.4 / 13.4
Calculating this gives us:
Total time ≈ 151.97 minutes
Now, we have the total time of the trip.
Average speed =total distance/ time taken
V=(v•t+tₒ)/(t+tₒ)
v=92 km/h =25.6 m/s.
V=78.6 km/h =21.8 m/s
tₒ=22 min=1320 s.
Plug in data and solve for ’t’