A BUS TRAVELS 280 KM SOUTH ALONG A STRAIGHT PATH WITH AN AVERAGE VELOCITY OF 88 KM/H TO THE SOUTH. THE BUS STOPS FOR 24MIN, THEN IT TRAVELS 210 KM SOUTH WITH AN AVERAGE VELOCITY OF 75 KM/H TO THE SOUTH.
A. HOW LONG DOES THE TOTAL TRIP LAST?
B.WHAT IS THE AVERAGE VELOCITY FOR THE TOTAL TRIP?
To solve this problem, we need to calculate the time taken for each leg of the trip and then find the total time. We also need to calculate the total distance traveled and the average velocity.
Let's break down the problem step by step:
Step 1: Calculate the time for the first leg.
Distance traveled in the first leg = 280 km
Average velocity for the first leg = 88 km/h
To find the time taken, we'll use the formula:
Time = Distance / Velocity
Time for the first leg = 280 km / 88 km/h = 3.18 hours (or 3 hours and 11 minutes)
Step 2: Calculate the time for the bus stop.
The bus stops for 24 minutes. We'll convert it to hours for consistency.
Time for the bus stop = 24 minutes / 60 minutes/hour = 0.4 hours
Step 3: Calculate the time for the second leg.
Distance traveled in the second leg = 210 km
Average velocity for the second leg = 75 km/h
Time for the second leg = 210 km / 75 km/h = 2.8 hours (or 2 hours and 48 minutes)
Step 4: Calculate the total time.
Total time = Time for the first leg + Time for the bus stop + Time for the second leg
Total time = 3.18 hours + 0.4 hours + 2.8 hours = 6.38 hours (or 6 hours and 23 minutes)
Therefore, the total trip lasts approximately 6 hours and 23 minutes. (Answer to part A)
Step 5: Calculate the total distance traveled.
Total distance = Distance of the first leg + Distance of the second leg
Total distance = 280 km + 210 km = 490 km
Step 6: Calculate the average velocity for the total trip.
Average velocity = Total distance / Total time
Average velocity = 490 km / 6.38 hours = 76.84 km/h (rounded to the nearest hundredth)
Therefore, the average velocity for the total trip is approximately 76.84 km/h (Answer to part B).
To find out the total duration of the trip, we need to calculate the time it takes for each leg of the trip separately.
For the first leg of the trip, the bus travels 280 km with an average velocity of 88 km/h. We can use the equation time = distance / velocity to find the time taken for this leg:
Time taken for the first leg = 280 km / 88 km/h = 3.18 hours
Next, we need to account for the 24-minute stop. To convert the minutes into hours, we divide by 60:
Stop time = 24 min / 60 = 0.4 hours
For the second leg of the trip, the bus travels 210 km with an average velocity of 75 km/h:
Time taken for the second leg = 210 km / 75 km/h = 2.8 hours
Now, we can find the total duration of the trip by adding the time taken for each leg and the stop time together:
Total duration of the trip = Time taken for the first leg + Stop time + Time taken for the second leg
= 3.18 hours + 0.4 hours + 2.8 hours
= 6.38 hours
Therefore, the total trip lasts approximately 6.38 hours.
To calculate the average velocity for the total trip, we need to find the total distance traveled and divide it by the total duration of the trip:
Total distance = Distance of the first leg + Distance of the second leg
= 280 km + 210 km
= 490 km
Average velocity = Total distance / Total duration of the trip
= 490 km / 6.38 hours
≈ 76.80 km/h
Therefore, the average velocity for the total trip is approximately 76.80 km/h.