Question

What is the new position of the drone relative to the top of the building?

Answer 1

The new position of the drone relative to the top of the building would be:

• 
  `-12(5)/(8)`

Hence, option (B) is correct.

Explanation:

Given that a drone flies up
`75(3)/(4)` ft above the top floor of a building.

As it flies away from the building and goes down
`117(7)/(8)`.

Thus, the new position becomes

`75(3)/(4)-117(7)/(8)`

`=(303)/(4)-117(7)/(8)`

`=(303)/(4)-(943)/(8)`

The LCM of 4,8: 8

Adjusting fractions based on LCM

`=(606)/(8)-(943)/(8)`

`\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)`

`=(606-943)/(8)`

`=-(337)/(8)`

Converting improper fractions to mixed numbers

`=-42(1)/(8)`

THEN IT RISES ANOTHER
`29(1)/(2)\:\:` and HOVERS onwards:

As the drone rises again another
`29(1)/(2)\:\:` ft, the final position can be calculated by adding
`29(1)/(2)\:\:` ft in
`-42(1)/(8)` ft.

i.e

`-42(1)/(8)+29(1)/(2)`

`=-(337)/(8)+29(1)/(2)`

`=-(337)/(8)+(59)/(2)`

The LCM of 8, 2: 8

Adjusting fractions based on LCM

`=-(337)/(8)+(236)/(8)`

`\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad (a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)`

`=(-337+236)/(8)`

`=-(101)/(8)`

Converting improper fractions to mixed numbers

`=-12(5)/(8)`

Therefore, the new position of the drone relative to the top of the building would be:

• 
  `-12(5)/(8)`

Hence, option (B) is correct.