A car travels at a constant speed of 30 mph for 20 miles, at a speed of 40 fps for the next 20 miles, and then travels the final 20 miles at 90 kph. what is the average speed of the entire trip?
d1 = V1*t1
t1 = d1/V1 = 20/30 = 0.667 h.
V2=40Ft/s * 1m1/5280Ft * 3600s/h = 27.3 mi/h.
t2 = d2/V2 = 20/27.3 = 0.733 h.
V3 = 90km/h * 1m1/1.6km = 56.3 mi/h.
t3 = d3/V3 = 20/56.3 = 0.355 h.
d = d1+d2+d3 = 20 + 20 + 20 = 60 mi.
T = t1+t2+t3 = 0.667 + 0.733 + 0.355 =
1.76 h.
V = d/T = 60mi/1.76h = 34.1 mi/h.
To find the average speed of the entire trip, we need to calculate the total distance traveled and the total time taken for the trip.
First, let's convert the speeds to a consistent unit. We can convert the speed of 30 mph to feet per second (fps) by multiplying by 5280/3600 (since 1 mile = 5280 feet and 1 hour = 3600 seconds).
30 mph * (5280 ft / 3600 s) = 44 fps
Next, let's convert the speed of 90 kph to feet per second. 1 kilometer = 0.621371 miles and 1 mile = 5280 feet. Therefore, we can convert 90 kph to miles per hour (mph) and then to fps.
90 kph * (0.621371 miles / 1 kilometer) * (1 hour / 60 minutes) * (1 minute / 60 seconds) * (5280 ft / 1 mile) = 66 fps
Now, let's calculate the time taken for each leg of the trip. Time (in seconds) can be calculated by dividing the distance by the speed.
For the first 20 miles (30 mph):
Time = Distance / Speed = 20 miles / 30 mph = 20 miles / 44 fps ≈ 0.4545 hours ≈ 27.27 minutes ≈ 1636.36 seconds
For the next 20 miles (40 fps):
Time = Distance / Speed = 20 miles / 40 fps = 0.5 hours = 30 minutes = 1800 seconds
For the final 20 miles (90 kph):
Time = Distance / Speed = 20 miles / 66 fps ≈ 0.3030 hours ≈ 18.18 minutes ≈ 1090.91 seconds
Now, let's calculate the total distance traveled:
Total Distance = 20 miles + 20 miles + 20 miles = 60 miles
Next, let's calculate the total time taken for the trip:
Total Time = 1636.36 seconds + 1800 seconds + 1090.91 seconds = 4527.27 seconds
Finally, to find the average speed, we divide the total distance by the total time:
Average Speed = Total Distance / Total Time = 60 miles / 4527.27 seconds ≈ 0.0132 miles per second ≈ 48 mph
Therefore, the average speed of the entire trip is approximately 48 mph.