A running time for movie a is 34 minutes more than twice the running time for movie b. If the running time for movie a is subtracted from triple the running time for movie b, the result is 60 minutes. Find the running times for each movie

The running for movie A is 81 minutes.

The running for movie B is 47 minutes.

Step-by-step explanation:

Let x represent the running for movie A.

Let y represent the running for movie B.

The running time for movie A is 34 minutes more than twice the running time for movie B.

This means that

x = y + 34

If the running time for movie A is subtracted from triple the running time for movie B, the result is 60 minutes. This means that

3y - x = 60 - - - - - - - - - - - - 1

Substituting x = y + 34 into equation 1, it becomes

3y - (y + 34) = 60

3y - y - 34 = 60

2y = 60 + 34

2y = 94

y = 94/2

y = 47

x = y + 34 = 47 + 34

x = 81

geometry: triangles

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answers archive

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+

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