i really need the answer quickly
1. Linda travels by car around one city to another with different constant speeds between pairs of cities. She travels for 35 min at 84 km/h, 17 min at 105 km/h and 50 min at 42 km/h and spends 25.0 min eating lunch and buying gas
a) Determine the average speed for the trip
b) Calculate the distance between the initial and final cities along the route
Total time spent driving or at stops:
= T = 35 + 17 + 50 + 25 = 127 minutes
(b) Total distance travelled:
= D = 84*(35/60) + 105*(17/60) + 42*(50/60) = 49 + 29.75 + 35 = 113.75 km
(a) Average speed = 113.75/127 = 0.89567 km/s = 53.74 km/h
To find the average speed for the trip (part a), we need to calculate the total distance traveled and divide it by the total time taken.
1. Convert the time durations to hours:
- 35 minutes = 35/60 = 0.5833 hours
- 17 minutes = 17/60 = 0.2833 hours
- 50 minutes = 50/60 = 0.8333 hours
- 25 minutes = 25/60 = 0.4167 hours
2. Calculate the distances traveled at each speed:
- Distance traveled at 84 km/h = 84 km/h * 0.5833 hours
- Distance traveled at 105 km/h = 105 km/h * 0.2833 hours
- Distance traveled at 42 km/h = 42 km/h * 0.8333 hours
3. Calculate the total distance traveled:
Total distance = Distance at 84 km/h + Distance at 105 km/h + Distance at 42 km/h
4. Calculate the total time taken:
Total time = Sum of all individual time durations (in hours) + Lunch and gas time (0.4167 hours)
5. Calculate the average speed:
Average speed = Total distance / Total time
To find the distance between the initial and final cities along the route (part b), we need to sum up the distances traveled at each speed.
Now let's plug in the values and calculate the answers step-by-step:
a) Determining the average speed for the trip:
- Distance traveled at 84 km/h = 84 km/h * 0.5833 hours = 48.9852 km
- Distance traveled at 105 km/h = 105 km/h * 0.2833 hours = 29.7985 km
- Distance traveled at 42 km/h = 42 km/h * 0.8333 hours = 34.9946 km
Total distance = 48.9852 km + 29.7985 km + 34.9946 km = 113.7783 km
Total time = 0.5833 hours + 0.2833 hours + 0.8333 hours + 0.4167 hours = 2.1166 hours
Average speed = Total distance / Total time
Average speed = 113.7783 km / 2.1166 hours
b) Calculating the distance between the initial and final cities along the route:
The distance between the initial and final cities is equal to the total distance traveled, which is 113.7783 km.
Therefore, the answers are:
a) The average speed for the trip is approximately ___ km/h (Calculate the result)
b) The distance between the initial and final cities along the route is approximately ___ km (Calculate the result)
To find the average speed for the trip, we need to use the formula Average Speed = Total Distance / Total Time.
To calculate the distance between the initial and final cities along the route, we need to add up the distances traveled at each speed.
First, let's find the total time traveled:
35 minutes + 17 minutes + 50 minutes + 25 minutes = 127 minutes
Convert the total time to hours:
127 minutes / 60 = 2.12 hours (rounded to two decimal places)
Now, let's find the total distance traveled:
Distance at 84 km/h = 84 km/h * 35 minutes / 60 = 49 km
Distance at 105 km/h = 105 km/h * 17 minutes / 60 = 29.75 km
Distance at 42 km/h = 42 km/h * 50 minutes / 60 = 35 km
Total distance = 49 km + 29.75 km + 35 km = 113.75 km
a) To determine the average speed, we divide the total distance by the total time:
Average Speed = Total Distance / Total Time
Average Speed = 113.75 km / 2.12 hours ≈ 53.68 km/h (rounded to two decimal places)
b) The distance between the initial and final cities is 113.75 km.