Question

John ran the​ 100-m dash with a time of 9.96 sec. If this pace could be maintained for an entire 26-mi ​marathon, what would his time​ be?

Answer 1

By calculating the average speed of a 100-meter dash and then applying it to the marathon distance, it would take approximately 1.16 hours, or 1 hour, 9 minutes, and 28 seconds to complete a 26-mile marathon at that pace.

Step-by-step explanation:

The student is asking how long it would take for someone to run a 26-mile marathon if they maintained the same speed as a 100-meter dash completed in 9.96 seconds. To calculate this, we first need to find the runner's average speed during the 100-meter dash. The speed (v) is distance (d) divided by time (t), so:

v = d / t = 100 meters / 9.96 seconds = 10.04 meters/second

Next, we convert the marathon distance from miles to meters. There are 1,609.34 meters in a mile, so:

26 miles * 1,609.34 meters/mile = 41,842.84 meters

To find the time (t) to run the marathon, we divide the total distance by the average speed:

t = 41,842.84 meters / 10.04 meters/second = 4,167.49 seconds

Finally, we convert seconds to a more understandable unit of time, hours and minutes:

4,167.49 seconds / 60 seconds/minute = 69.46 minutes
69.46 minutes / 60 minutes/hour ≈ 1.16 hours

So, John would complete the marathon in approximately 1.16 hours, or 1 hour, 9 minutes, and 28 seconds if he could maintain his 100-meter dash pace for the entire marathon.

Answer 2

we know that
1 mile----------------> 1609.34 meters
26 miles---------------> X
X=26*1609.34=41842.84 m

I apply a rule of three to know the time

if 100 m---------------9.96 sec
41842.84 m----------> x
x=41842.84*9.96/100=4167.5468 sec

to get minutes I divide it by 60---------> 4167.5468/60=69.459113 minutes

to get hours I divide it by 60----------> 69.459113/60=1.1576518 hours

1.1576518= 1 hour 9 minutes 27.55 sec

the answer is 1 hour 9 minutes 27.55 sec------->(4167.5468 sec)