It takes a runner 3 h, 10 min, 55 s to run a marathon. If the distance of a marathon is 42.2 km, what is the average speed of the runner?
ttime = 3 + 10/60 + 55/3600 hours
so
speed = 42.2 / (3+10/60+55/3600)
in km/hr
To find the average speed of the runner, we can use the formula:
Average speed = Distance / Time
We are given that the distance of a marathon is 42.2 km, and the time taken by the runner is 3 hours, 10 minutes, and 55 seconds.
First, we need to convert the time to a decimal format. There are 60 minutes in an hour and 60 seconds in a minute. So, 10 minutes is equal to 10/60 = 1/6 hours. Similarly, 55 seconds is equal to 55/3600 ≈ 15/1000 hours.
Now, we can convert the total time to hours by adding the converted minutes and seconds:
Total time = 3 hours + 1/6 hours + 15/1000 hours
Next, we can simplify the fractions:
Total time = 3 hours + 10/60 hours + 55/3600 hours
Convert all fractions to a common denominator:
Total time = 3 hours + 1/6 hours + 1/120 hours
Now, add all the terms:
Total time = (3*120 + 20 + 1)/120 hours
Total time = 361/120 hours
Finally, we can calculate the average speed:
Average speed = Distance / Time
Average speed = 42.2 km / (361/120) hours
To divide by a fraction, we can multiply by its reciprocal:
Average speed = 42.2 km * (120/361) km/h
Now, calculate the expression:
Average speed = (42.2 * 120) / 361 km/h
Average speed ≈ 14.07 km/h
Therefore, the average speed of the runner is approximately 14.07 km/h.