a. T=290km/81km/h + 210km/80km/h + 25/60 = 6.62 h.
b. V = d/T = (290+210)/6.62 = 75.5 km/h.
b. V = d/T = (290+210)/6.62 = 75.5 km/h.
First, let's calculate the time taken for the bus to travel 290 km at an average velocity of 81 km/h:
We can use the formula: time = distance / velocity
So, the time taken for the first leg of the trip is:
time = 290 km / 81 km/h ≈ 3.58 hours
Next, let's calculate the time taken for the bus to travel 210 km at an average velocity of 80 km/h:
Again, using the formula: time = distance / velocity
So, the time taken for the second leg of the trip is:
time = 210 km / 80 km/h ≈ 2.63 hours
Now, let's find the total time of the trip by adding the times for the two legs:
total time = 3.58 hours + 2.63 hours ≈ 6.21 hours
Therefore, the trip lasts approximately 6.21 hours.
To find the average velocity for the total trip, we need to calculate the total distance traveled and the total time taken:
The total distance traveled is 290 km + 210 km = 500 km
The total time taken is 6.21 hours
Now, we can use the formula: average velocity = total distance / total time
So, the average velocity for the total trip is:
average velocity = 500 km / 6.21 hours ≈ 80.32 km/h
Therefore, the average velocity for the total trip is approximately 80.32 km/h.