SOLUTION: a railroad bridge is built over a v-shaped canyon. if the supports are 2 feet long at each end, the center support is 422 feet long, and the supports increase in length by 3 feet e

Question 1034236: a railroad bridge is built over a v-shaped canyon. if the supports are 2 feet long at each end, the center support is 422 feet long, and the supports increase in length by 3 feet each support, what is the total length of all supports?
Answer by ikleyn(52824) (Show Source): You can put this solution on YOUR website!
.
a railroad bridge is built over a v-shaped canyon. if the supports are 2 feet long at each end, the center support is 422 feet long,
and the supports increase in length by 3 feet each support, what is the total length of all supports?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

There are  = 140 supports on one side with the lengths from 2 feet to 419 feet long, 
and there is the same amount of 140 supports on the other side. Plus one central support of 422 feet long.

Combine 

   2 +   5 +   8 + . . . + 419 + 422
+
 419 + 416 + 413 + . . . +   2

--------------------------------

 422 + 422 + 422 + . . . + 422 + 422


422 feet taken 141 times. You will get the combined length 422*141 = 59502 feet, in total.

It is the "Gauss' method" for summing up an arithmetic progression.

RELATED QUESTIONS
A railroad bridge is built over a V-shaped canyon. If the supports are 3 feet long at... (answered by greenestamps)

A railroad crosses a highway over an arch a cross section of which is an semi-ellipse 42... (answered by ikleyn)

Can you show me how to do this problem? A pedestrian bridge is to be built over... (answered by Fombitz)

The cable for a suspension bridge is shaped like a parabola. The towers are 100 ft tall... (answered by ankor@dixie-net.com)

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196... (answered by ankor@dixie-net.com)

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174... (answered by Fombitz)

A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 152... (answered by greenestamps)

The cable of a horizontal suspension bridge are supported by two towers 120 feet apart... (answered by Alan3354,ikleyn)

a bus of total weight 20000n is packed 5m from one end of a bridge of uniform weight... (answered by Fombitz)