Help with this please. No idea.
Except for a 22.00 min. rest stop, Emily drives with a constant velocity of 89.5 km/hr north. How long does the trip take if Emily's average velocity is 77.8 km/hr north?
t = actual time racing along the road
22/60 = .367 hour
tend - tbegin = (t +.367)hr
and
d/(t+.367) = 77.8
but
d/t 89.5
so
d = 89.5 t
and
89.5 t/(t+.367) = 77.8
89.5 t = 77.8 t + 28.5
t = 2.438 hr driving
t+ .367 = 2.805 hr
= 2 hours and 49 minutes
To solve this problem, we can use the formula for average velocity:
Average velocity = total displacement / total time
In this case, the average velocity is given as 77.8 km/hr north. We need to find the total time taken for the trip.
Let's assume the total time for the trip is T hours. During this time, Emily drives at a constant velocity of 89.5 km/hr north, except for the 22.00 min rest stop.
To calculate the total time, we need to consider two parts of the trip: the driving time and the rest time.
1. Driving Time:
During the driving time, Emily travels at a constant velocity of 89.5 km/hr north. So, the distance she covers is 89.5 km/hr x T hr = 89.5T km.
2. Rest Time:
Emily takes a rest stop of 22.00 min, which is equal to 22.00/60 hr = 0.367 hr. During this time, she does not cover any distance.
Now, let's calculate the total time for the trip:
Total time = Driving time + Rest time
= T hr + 0.367 hr
Since the average velocity is given by average velocity = total displacement / total time, we can set up the equation:
77.8 km/hr = (89.5T km) / (T + 0.367 hr)
Now, let's solve for T:
77.8(T + 0.367) = 89.5T
77.8T + 28.5 = 89.5T
11.7T = 28.5
T = 28.5 / 11.7
T ≈ 2.44 hr
Therefore, the total time for the trip is approximately 2.44 hours.
To find the time it takes for the trip, we can use the formula:
Time = Distance / Velocity
First, let's calculate the distance covered during the trip by subtracting the rest stop time. The rest stop lasts for 22.00 minutes, which is equivalent to 22.00 / 60 = 0.367 hours.
Hence, the time spent driving is the total time minus the rest stop time:
Time driving = Time - Rest stop time
= Time - 0.367
Now, we can use the formula for average velocity to find the time it takes for the trip with the given average velocity:
Average Velocity = Total Distance / Time
Since we already know the average velocity (77.8 km/hr) and the time spent driving (Time - 0.367), we can rearrange the formula as follows:
Time - 0.367 = Total Distance / Average Velocity
Rearranging the equation to solve for the total distance:
Total Distance = Average Velocity * (Time - 0.367)
Now, we can substitute the given velocity (89.5 km/hr) into the equation and solve for Time:
Total Distance = 89.5 km/hr * (Time - 0.367)
Now, we have an equation with only one unknown, Time. We can solve it:
Total Distance = 89.5 km/hr * Time - 89.5 km/hr * 0.367
Given that the average velocity is the total distance divided by the time:
77.8 km/hr = Total Distance / Time
Now, substitute the value of Total Distance from the previous equation:
77.8 km/hr = (89.5 km/hr * Time - 89.5 km/hr * 0.367) / Time
To simplify further, distribute the velocity:
77.8 km/hr = 89.5 km/hr - 89.5 km/hr * 0.367 / Time
Now, isolate Time:
77.8 km/hr * Time = 89.5 km/hr - 89.5 km/hr * 0.367
Multiply both sides by Time:
77.8 km/hr * Time^2 = 89.5 km/hr * Time - 89.5 km/hr * 0.367 * Time
Rearrange the equation and apply the distributive property:
77.8 km/hr * Time^2 - 89.5 km/hr * Time + 89.5 km/hr * 0.367 * Time = 0
Now, we have a quadratic equation. We can solve it using various methods, such as factoring, completing the square, or using the quadratic formula. Solving the equation will give us the value of the Time variable.