Question

a flashlight can shine brightly for 10 hours or dimly for 100 hours. if it shines brightly for 3 hours and shines dimly for 40 hours, how many more hours can it shine dimly?
a 24 hours
25 hours
c 28 hours
d 30 hours

Explanation:

Step1: Define battery capacity

Let total battery capacity = $C$.
Bright mode rate: $\frac{C}{10}$ per hour
Dim mode rate: $\frac{C}{100}$ per hour

Step2: Calculate used capacity

Used capacity = (Bright use × rate) + (Dim use × rate)
$Used = 3 \times \frac{C}{10} + 40 \times \frac{C}{100}$
$Used = \frac{3C}{10} + \frac{40C}{100} = \frac{30C}{100} + \frac{40C}{100} = \frac{70C}{100} = 0.7C$

Step3: Find remaining capacity

$Remaining = C - 0.7C = 0.3C$

Step4: Calculate remaining dim hours

Hours = $\frac{Remaining}{\text{Dim rate}} = \frac{0.3C}{\frac{C}{100}} = 0.3 \times 100 = 30$

Answer:

D 30 hours