In a 5.00 km race, one runner runs at a steady 11.3 km/h and another runs at 14.9 km/h .
How long does the faster runner have to wait at the finish line to see the slower runner cross?
t1 = 5/11.3 = .4425 hour
t2 = 5/14.9 = .3356 hour
waiting time = difference= .1069 hr
= 6.415 minutes
= 6 minutes and 25 seeconds
To find out how long the faster runner has to wait at the finish line for the slower runner to cross, we first need to calculate the time it takes for each runner to finish the race.
We can use the formula: time = distance / speed.
For the slower runner:
distance = 5.00 km
speed = 11.3 km/h
Time taken by the slower runner = 5.00 km / 11.3 km/h
To divide kilometers by kilometers per hour, we need to convert hours to minutes. We know that 1 hour has 60 minutes. So we can multiply the time in hours by 60 to get the time in minutes.
Time taken by the slower runner = (5.00 km / 11.3 km/h) * (60 min/h)
Now, let's calculate the time taken by the slower runner.
Time taken by the slower runner = (5.00 km / 11.3 km/h) * (60 min/h)
= 26.55 minutes (rounded to two decimal places)
Therefore, the slower runner takes approximately 26.55 minutes to finish the race.
Now, let's calculate the time it would take for the faster runner to finish the race.
For the faster runner:
distance = 5.00 km
speed = 14.9 km/h
Time taken by the faster runner = 5.00 km / 14.9 km/h
Again, we need to convert hours to minutes.
Time taken by the faster runner = (5.00 km / 14.9 km/h) * (60 min/h)
= 20.13 minutes (rounded to two decimal places)
Therefore, the faster runner takes approximately 20.13 minutes to finish the race.
Now, to find out how long the faster runner has to wait at the finish line, we subtract the time taken by the slower runner from the time taken by the faster runner.
Waiting time = Time taken by the faster runner - Time taken by the slower runner
= 20.13 minutes - 26.55 minutes
= -6.42 minutes (rounded to two decimal places)
Since we have a negative waiting time, it means that the faster runner would already have finished the race by the time the slower runner crosses the finish line. Therefore, the faster runner does not have to wait at the finish line for the slower runner to cross.