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

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!