A drone's battery charge is at 98\% when it begins a mission. During the mission, the batt… — SAT

A drone's battery charge is at $98\%$ when it begins a mission. During the mission, the battery charge decreases by $1.5\%$ per minute when the drone is hovering, and by $2.5\%$ per minute when it is flying horizontally. The drone flies horizontally for exactly twice as many minutes as it hovers. If the battery charge is at $33\%$ at the end of the mission, for how many minutes did the drone hover?

Cevap: 10 minutes

Cevap

The drone hovered for 10 minutes.

Let

t

represent the number of minutes the drone hovers. Since the drone flies horizontally for twice as long as it hovers, it flies horizontally for

2t

minutes. The total percentage drop in battery is

98 - 33 = 65

. The equation representing the total decrease in battery charge is

1.5t + 2.5(2t) = 65

. Simplifying the equation yields

1.5t + 5t = 65

, which becomes

6.5t = 65

. Dividing both sides of the equation by

6.5

gives

t = 10

Adım Adım Çözüm

Define the variable for the unknown quantity.

Let

t

be the number of minutes the drone spent hovering. The time spent flying horizontally is then

2t

minutes.

The problem states that the horizontal flight time is exactly twice the hovering time.

Set up an equation representing the total decrease in battery charge.

The total percentage decrease is

1.5t + 2.5(2t) = 98 - 33

The battery decreases by

1.5\%

per minute of hovering,

2.5\%

per minute of horizontal flight, and the total change is from

98\%

33\%

Simplify the equation and solve for

t

6.5t = 65

, which gives

t = 10

Combine like terms and divide both sides by

6.5

to isolate the variable.

Anahtar Kavram

Setting up and solving a linear equation in one variable from a real-world scenario.

Soru

Cevap

Adım Adım Çözüm

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