Question

The Olympic record for the marathon is 2.00h, 9.00 min, 21.0 s. If the average speed of a runner achieving this record is 5.436 m/s, what is the marathon distance?

Help me someone please..

Answer 1

Distance = speed * time

T = 2 hours, 9 min 21 s, we convert it all to seconds.

1 hour = 60*60 s, 1min = 60s

2*60 *60 = 7200s
9*60 = 540s
21s

Total = 7200 + 540 + 21 = 7761s

Distance = speed * time = 5.436 m/s * 7761s = 42188.796m

Distance = 42188.796 m

Of course this is on the assumption that the speed of the runner was the same all through the race.

Of course it is not humanly possible to maintain same speed all through race, there would some slightly speeding up or slowing down.

Answer 2

Distance = (speed) x (time)

(2.00 hours) x (3,600 seconds/hour) = 7,200 seconds
(9.00 minutes) x (60 seconds/minute) = 540 seconds
(21.0 seconds) x (1 second/second) = 21 seconds
_______________
Total time = (7,200 + 540 + 21) = 7,761 seconds


Distance = (5.436 m/s) x (7,761 s) = 42,188.796 meters

= 42.189 kilometers

Whoa ! The official Olympic marathon distance: 42.195 km .
My answer is 0.021% too short.
Should this answer be marked right or wrong ?

Well . . .

-- If the official marathon distance is run in the given time,
then the speed would be closer to 5.4368 m/s.

-- If the official marathon distance is run at the given speed,
then it would take 2hr 9min 22.1sec.

So the discrepancy of 6 meters implies a discrepancy of
either 0.0008 m/s in the given speed, or else a discrepancy
of 1.1 second in the given time, compared to the numbers
in the question.

I claim that my answer should be marked 'correct'.
The results are within experimental uncertainty for a scientist,
and absolutely nailed beautifully on the button for an Engineer !