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Difficulty: MediumSolving Linear Equations

A delivery drone starts a flight with a battery charge of 95%95\%. The battery charge decreases at a constant rate of 1.5%1.5\% per minute of flight time. During the flight, the drone lands on a charging station for 1515 minutes, during which its battery charge increases at a constant rate of 2.4%2.4\% per minute. After this charging period, the drone resumes its flight. If the drone ends its flight with a battery charge of 65%65\%, and its total flight time (excluding the time spent charging) was tt minutes, what is the value of tt?

Answer: 44 minutes

Answer

44
The correct answer is found by setting up a linear equation that models the drone's battery charge changes. The drone starts with 95%95\% battery, loses 1.5%1.5\% per minute for tt minutes, and gains 36%36\% from charging (15×2.4%15 \times 2.4\%). Setting this equal to the final charge of 65%65\% gives the equation 95−1.5t+36=6595 - 1.5t + 36 = 65. Simplifying gives 131−1.5t=65131 - 1.5t = 65, which leads to −1.5t=−66-1.5t = -66 and t=44t = 44.

Step-by-Step Solution

1
Calculate the total percentage of battery charge gained while charging.
36%36\%
The drone charges at a rate of 2.4%2.4\% per minute for 1515 minutes, so the total gain is 15×2.4%=36%15 \times 2.4\% = 36\%.
2
Set up a linear equation for the final battery charge.
95−1.5t+36=6595 - 1.5t + 36 = 65
The final battery charge (65%65\%) is the initial charge (95%95\%) minus the battery consumed during flight (1.5%1.5\% per minute for tt minutes) plus the charge gained (36%36\%).
3
Combine constant terms on the left side of the equation.
131−1.5t=65131 - 1.5t = 65
Adding 9595 and 3636 simplifies the expression on the left side.
4
Isolate the variable term by subtracting 131131 from both sides.
−1.5t=−66-1.5t = -66
Subtracting 131131 from both sides leaves only the variable term on the left.
5
Divide both sides by −1.5-1.5 to solve for tt.
t=44t = 44
Dividing −66-66 by −1.5-1.5 isolates tt to find the total flight time.

Key Concept

Solving linear equations in a real-world context by setting up an algebraic equation.
Estimated Time:1m 30s
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Topics

Solving Linear Equations

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