A car needs to go 55 miles It travels 55mph for the first mi

A car needs to go 55 miles. It travels 55mph for the first mile, then slows 1 mile per hr. each mile traveled. How long will it take the car to go the 55 miles?

Solution

The sequence of speeds are:

55,54,53...,3,2,1

Using the formula TIME=%28DISTANCE%29%2F%28SPEED%29,

the sequence of times is

1%2F55,1%2F54,1%2F53,...1%2F3,1%2F2,1%2F1

So the total time is:

1%2F55%2B1%2F54%2B1%2F53%2B%27...%27%2B1%2F3%2B1%2F2%2B1%2F1

This is called a finite harmonic series, i.e., a sum of the
reciprocals of an arithmetic sequence. There is no formula but by
use of technology we find that the sum is approximately
4.593612212 hours.

You can do it on a TI-84,

Press CLEAR
Press 2nd
Press STAT
Press the right arrow
Press the right arrow again
Press 5

You should see this ---> sum(

Press (

You should see this ---> sum((

Press 2nd
Press STAT
Press the right arrow
Press 5

You should see this ---> sum((seq(

Type 1/X,X,55,1,-1))

You should see this ---> sum((seq(1/X,X,55,1,-1))

Press ENTER

Read 4.593612212