## The population at tinyville is 16.2 tinys per acre. Exactly 405 tinys live in tinyville. How many acres is tinyville?

October 12, 2019// Blog//

Answer: 44 miles

WORKINGS

Given,

The distance between Indianapolis and Lima, IL = 173 miles

The distance between Indianapolis and Dayton, ID = 165 miles

The distance between Dayton and Lima, DL is unknown

Since there are straight roads connecting the three cities, the connection between them form a right angles triangle.

The right angle is at Dayton

The hypotenuse is the distance between Indianapolis and Lima, IL

Therefore IL^2 = ID^2 + DL^2

173^2 = 165^2 + DL^2

DL^2 = 173^2 – 165^2

DL^2 = 29929 – 27225

DL^2 = 2704

DL = 52 miles

Therefore, The distance between Dayton and Lima, DL = 52 miles

The question is asking how many more miles would Meg drive if she stopped in Dayton first than if she drove directly to Lima.

That is, Distance of Indianapolis to Dayton + Distance of Dayton to Lima – Direct distance of Indianapolis to Lima

That is, ID + DL – IL

= 165 miles + 52 miles – 173 miles

= 217 miles – 173 miles

= 44 miles

Therefore, Meg would drive 44 more miles if she stopped in Dayton first than if she drove directly to Lima.