Please help with word problem!!!

Question

On my recent drive to the Outer Banks for Spring Break, I happened to notice a sign indicating that, for the next four miles, the road would be descending at a 6% grade.

After four miles I noticed a second sign that indicated that for the next five miles, we would be descending at a 4% grade.

If we were at 10,000 feet above sea level when I noticed the first sign, how many feet above sea level will the car be when it reaches the end of the five miles indicated by the second sign?

Note: A 6% grade means that the road descends 6 feet for every 100 feet traveled. A 4% grade means that the road descends 4 feet for every 100 feet traveled.

Answer 1

"A 6% grade means that the road descends 6 feet for every 100 feet traveled."

    You traveled 4 miles =

          (5280 ft/mi)*(4 mi)

              21120 ft

    A 6% grade is:

             (6/100)*(21120 ft) =

                      1267.2 ft 

 

At that point, the elevation is:

        10,000 ft - 1267 ft =  8733 ft     (rounded)

 

Now, going 5 miles =

              (5280 ft/mi)(5 mi)

                26400 ft

     A 4% grade is:

            (4/100)*(26400 ft) =

                1056 ft

 

At that point, the elevation is:

         8733 ft - 1056 ft =

              7677 ft     (rounded)

               

Answer 2

Four miles equals 21,120 feet.

In the first four miles you descend 0.06(21120), or 1267.2 feet

Five miles equals 26,400 feet.

In the next five miles you descents 0.04(26400), or 1056 feet

 

10000 - 1267.2 - 1056 = 7676.8

 

Your ending elevation is seven thousand six hundred seventy-six and eight tenths feet.