Distance - Miles Plowed - Furrows

[Guest]

A rectangular field is plowed with furrows 15 in. wide. The field is 30 rods wide and length is 10 rods less than it's diagonal. Determine number of miles traveled.


15 in. = 1.25 ft. = 0.00024 mi.

30 rods = 495 ft. = 0.09375 mi.

Diagonal of rectangle - sq. root (length^2 + width^2)

width^2 - 30^2 = 900

495 x 1.25 = 618.75 = 619 ft.

How do I proceed ?

[Guest]

Why not do it exactly the same as other similar problems on this forum........
Find the area, then how far travelled per unit area plowed, then find how many of these units in total area to be plowed......

Width squared + Length(L) Squared = Diagonal Squared .... and diagonal is (Length + 10)
30^2 + L^2 = (L + 10)^2
30^2 + L^2 = L^2 + 20L + 100
900 = 20L + 100
20L = 800
L = 40
Area = 30 x 40 = 1200 sq. rods

1 rod = 5.5 yards = 16.5 feet ....1 sq rod = 272.25 sq feet
Then the Area = 1200 x 272.25 = 326700 sq.feet
Furrow = 15 inches = 1.25 feet so every foot travelled there will be 1.25 sq.feet of area plowed.

Total Number of feet travelled will be 326700 / 1.25 = 261360 feet.
Total Number of miles travelled will be 261360 / 5280 = 49.5 miles.

[Guest]

Thanks. I was not sure how to calculate the area, then solve the remainder.

[Guest]

A question:

How did you get the 20L ?

[Guest]

How I got the 20L
Write it as product of 2 brackets and multiply each term in one bracket on each term in the other bracket.

(L + 10)^2
= (L + 10)(L + 10)
= (L x L) + (L x 10) + (10 x L) + (10 x 10)
= L^2 + 10L + 10L + 100
= L^2 + 20L + 100

Some people use "FOIL" .....means multiply "FIRSTS" then "OUTERS" then "INNERS" then "LASTS" in each bracket
= (L x L)......"FIRSTS"
+ (L x 10) ....."OUTERS"
+ (10 x L)......."INNERS"
+ (10 x 10)......"LASTS"
and add them up...............

[Guest]

I understand now. Thanks.