A videotape can record 2 hours on short play, 4 hours on long play, or 6 hours on extra long play. After recording 32 minutes on short play and 44 minutes on long play, how many minutes can it record on extra-long play

It can record 198 mintues on extra-long play

Step-by-step explanation:

The full battery(100%) of the videotape is:

2 hours(120 minutes) on short play

4 hours(240 minutes) on long play

6 hours(360 minutes) on extra long play.

32 minutes on short play

It used 32/120 = 0.2667 of the battery

44 minutes on long play

it used 44/240 = 0.1833 of the battery

Battery used:

0.2667 + 0.1833 = 0.45

Battery remaining

1 - 0.45 = 0.55

Out of 6 hours(360) on long play

0.55*360 = 198

It can record 198 mintues on extra-long play

geometry: triangles

solvers

lessons

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+

25.45584