Question

2. A long distance runner runs 6.5 miles in the first hour of a race. The distance covered in each subsequent hour is 95% of the distance covered in the previous hour.
How far does the long distance runner run in 5 hours?
Round your answer to the nearest hundredth of a mile.

Answer 1

Answer: Ok. This is not the answer. LOL. Can you help on social studes quiz???

Step-by-step explanation:

Answer 2

Hello!

The answer is: 27.92 miles

Why?

We know that the runner can run 6.5 miles in the first hour of a race, after that, each subsequent hour the distance is 95% of the distance covered in the previous hour.

We can calculate how far does the long distance runner run in 5 hours using the following equation and evaluating it from 1 to 5 hours:

$D_{t} =D_{o}*(0.95)^{t}$

Where,

$D_{t}=TotalDistance\\D_{o}=DistancePerHour\\t=time(hours)$

So, calculating how far does the long distance runner run in 5 hours, we have:

$D_{5} =6.5*(0.95)^{1}+6.5*(0.95)^{2}+6.5*(0.95)^{3}+6.5*(0.95)^{4}+6.5*(0.95)^{5}\\\\D_{5}=6.18+5.87+5.57+5.29+5.03=27.92miles$

Hence, the runner ran 27.92 miles after 5 hours.

Have a nice day!