in a triathlon , an athlete swims 750m in 15 minutes, cycles at an average speed of 40km/h for 30 minutes and runs 5 km at an average speed of 3m/s . find his average speed for the entire competition giving your answer in km/h
avg speed is total distance divided by total time. So, expressing all distances in km, and all times in hours, and recalling that
time = distance/speed
(0.750 + (40 * 1/2) + 5)km/(0.25 + 0.5 + 5000/3 * 1/3600)hr
= 21.229 km/hr
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To find the average speed for the entire competition, we need to calculate the total distance traveled by the athlete and the total time taken for the entire triathlon.
The distance traveled by the athlete in the swimming portion is 750m.
The time taken for swimming is 15 minutes, which is equal to 15/60 = 0.25 hours.
The distance traveled by the athlete in the cycling portion can be calculated using the average speed and time taken. The formula for distance is given by distance = speed × time.
Distance = 40 km/h × 30 minutes = 40/60 × 30 = 20 km.
The distance traveled by the athlete in the running portion is 5 km.
The time taken for running can be calculated using the average speed and distance. The formula for time is given by time = distance / speed.
Time = 5 km / 3 m/s = 5000 m / (3 × 1000) km/s = 5/3 km / 3 km/s = 5/9 s.
Now, let's calculate the total distance and total time for the entire triathlon.
Total distance = swimming distance + cycling distance + running distance
Total distance = 750m + 20 km + 5 km = 750m + 20000m + 5000m = 25750m.
Total time = swimming time + cycling time + running time
Total time = 0.25 hours + 0.5 hours + 5/9 hours = (0.25 + 0.5 + 5/9) hours.
Finally, we can calculate the average speed for the entire competition using the formula average speed = total distance / total time.
Average speed = 25.75 km / (0.25 + 0.5 + 5/9) hours.
To simplify the calculation, we can convert the total time into minutes.
Average speed = 25.75 km / ((0.25 + 0.5 + 5/9) × 60) minutes.
Calculating the value, the average speed for the entire competition is 27.98 km/h (rounded to two decimal places).
To find the average speed for the entire competition, we need to calculate the total distance covered and the total time taken.
Let's start by converting the distances to a consistent unit. We know that 1 kilometer (km) is equal to 1000 meters (m).
The athlete swims a distance of 750m in 15 minutes. Converting this to kilometers, we divide 750m by 1000 to get 0.75km. The time remains the same at 15 minutes.
Next, the athlete cycles at an average speed of 40km/h for 30 minutes. The distance covered can be calculated by multiplying the speed by time, which is 40km/h * 30 minutes = 1200km.
Finally, the athlete runs a distance of 5km at an average speed of 3m/s. We need to convert the speed to km/h by multiplying it by (60/1000) since there are 60 minutes in an hour and 1000 meters in a kilometer. So, 3m/s * (60/1000) = 0.18km/h. The distance remains the same at 5km.
Now, let's calculate the total distance covered:
Total distance = swimming distance + cycling distance + running distance
Total distance = 0.75km + 1200km + 5km = 1205.75km
Next, we'll calculate the total time taken:
Total time = swimming time + cycling time + running time
Total time = 15 minutes + 30 minutes = 45 minutes
Finally, we can find the average speed by dividing the total distance by the total time:
Average speed = Total distance / Total time
Average speed = 1205.75km / 45 minutes
To convert the speed to km/h, we multiply it by (60/1) since there are 60 minutes in an hour and 1 hour in an hour. So, (1205.75km / 45 minutes) * (60/1) = 1614 km/h.
Therefore, the athlete's average speed for the entire competition is 1614 km/h.