An antelope has traveled 1.60 km at avg speed of 67.0 km/h. The antelope speed during the first half of the distance is 88km/h. Find the antelope's avg speed during the second half of the run.
The time is the distance divided by the velocity. The total time is the time at 88km/h + the time at the unknown speed v. Half the distance is run at each speed:
0.8/88 + 0.8/v = 1.6/67
.009091 + 0.8/v = .02388
.8/v = 0.01365
v = 58.6 km/h
To find the average speed during the second half of the run, we first need to determine the time it took for the antelope to travel the entire distance.
We can use the formula: Speed = Distance ÷ Time
Given:
Distance traveled = 1.60 km
Overall average speed = 67.0 km/h
Let's denote the average speed during the second half of the run as 'x' km/h.
First, we find the time taken to travel the entire distance:
Time = Distance ÷ Speed
Time = 1.60 km ÷ 67.0 km/h
Time = 0.0239 hours
Next, let's denote the time taken to travel the first half of the distance as 't' hours.
Since the antelope's speed during the first half of the distance is 88 km/h, we can write:
t = Distance of the first half ÷ Speed of the first half
t = 0.80 km ÷ 88 km/h
t = 0.0091 hours
Now, we can calculate the time taken to travel the second half of the distance by subtracting 't' from the total time:
Time taken for the second half = Total time - Time taken for the first half
Time taken for the second half = 0.0239 hours - 0.0091 hours
Time taken for the second half = 0.0148 hours
Finally, we can find the average speed during the second half of the run by using the formula:
Average speed = Distance ÷ Time
Average speed = 0.80 km ÷ 0.0148 hours
Average speed = 54.05 km/h (rounded to two decimal places)
Therefore, the antelope's average speed during the second half of the run is approximately 54.05 km/h
To find the antelope's average speed during the second half of the run, we need to first determine how long it took the antelope to travel the first half of the distance.
We know that the antelope traveled a distance of 1.60 km at an average speed of 67.0 km/h. To find the time it took to travel this distance, we can use the formula:
time = distance / speed
Plugging in the values, we have:
time = 1.60 km / 67.0 km/h
Simplifying the equation, we have:
time ≈ 0.0239 hours (rounded to four decimal places)
Now, we know that the antelope's speed during the first half of the distance is 88 km/h. So, we can determine the time it took for the antelope to travel the first half of the distance using the formula:
time = distance / speed
Plugging in the values, we have:
time = 1.60 km / 88 km/h
Simplifying the equation, we have:
time ≈ 0.0182 hours (rounded to four decimal places)
Next, we can find the time it took the antelope to travel the second half of the distance by subtracting the time it took for the antelope to travel the first half from the total time it took to travel the entire distance:
total time - time for first half = time for second half
0.0239 hours - 0.0182 hours = 0.0057 hours (rounded to four decimal places)
Finally, to find the average speed during the second half of the run, we can use the formula:
speed = distance / time
Plugging in the values, we have:
speed = 1.60 km / 0.0057 hours
Simplifying the equation, we have:
speed ≈ 280.7 km/h (rounded to one decimal place)
Therefore, the antelope's average speed during the second half of the run is approximately 280.7 km/h.