Scale and Scale Factor Help?

1)Find the map distance if the actual distance is 660 and the scale on the map is 1 inch=240 miles.



2) The St. Louis arch is 210 yards tall. A model of the arch is 9 feet. What are the scale and the scale factor of the model?



Thanks, and please tell me how you got the answer.Scale and Scale Factor Help?
i had to do a test on this



basically formula goes is that...



An=Ao x k



so it's something like the area of the new=the area of the old multiplied by the scale factor



Q1: An=660 miles - (oh and you did not tell the units of 660 btw :)

Ao=?

k=240 miles



so it's like 660= Ao x 240



660/240= (to isolate Ao)

Ao=2.75 inches

the map is 2.75 inches



2. An=210 yards

Ao=9 feet

k=?



now the thing is that i am canadian and deal with the metric system lol

but i'll try it anyways



1 yard=3 feet



210 yards=9 feet x k



210 yards= 3 feet x k



oh and the reason why you had to convert is because the last one dealt with two numbers that had the same unit



so isolate k you have to divide 3 feet on both sides



you are left with:



k=70 yards



so the scale factor for this one is 70 yards



this is from me and no i am not a math teacher so i may be wrong

but i think this is how you do it

i remember kids at school asking me how to do this too lol :)

but i hope you get this now



and remember...



An=Ao x k

Area of the new is equal to the area of the old multiplied by the scale factor
1) 1/x = 240/660 thus 240X = 660. divide 660 by 240 for 2.75" on the map



2) Convert the 210 yards to feet and then divide by the model size.

210 x 3 = 630 630/9. Each foot on the model equals 70 feet on the arch.Scale and Scale Factor Help?
1. 1''=240 miles; 660/240=2 3/4 inches

2.9 feet= 3 yards; model=3yards, St. Louis arch is210yards

210/3=70

scale is 1:70