John can finish a paper route in 4 hours, and Andrew
can finish the same paper route in 7 hours. If they work together,
how long would it take them to finish the paper route?

in one hour, John does 1/5 of the route and Andrew does 1/7

Together, they do 1/x of the whole route, x being unknown.

(1/5)+(1/7)=(1/x) Multiply everything by 35x, the common denominator

7x+5x+35

12x=35

x=35/12 or 2 11/12 hours, or 2h55m

Step-by-step explanation:

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584