A high-speed digital camera records 480 frames every 3 seconds. The camera operator increa… — ACT

A high-speed digital camera records $480$ frames every $3$ seconds. The camera operator increases the recording rate by $25\%$ . At this new recording rate, how many total frames will the camera record in $14$ seconds?

A
$1,680$
B
$2,240$
$2,800$ Answer
D
$3,920$
E
$8,400$

Answer

The camera will record 2,800 frames in 14 seconds at the new recording rate.

To solve this problem, first determine the initial frame rate:

480

frames divided by

3

seconds equals

160

frames per second. Increasing this rate by

25\%

produces

160 \times 1.25 = 200

frames per second. Multiplying the new rate by

14

seconds results in

200 \times 14 = 2,800

frames.

Step-by-Step Solution

Calculate the original unit rate in frames per second.

\frac{480 \text{ frames}}{3 \text{ seconds}} = 160 \text{ frames per second}

Dividing the number of frames by the elapsed time yields the frame rate per second.

Determine the new unit rate after a

25\%

increase.

160 \times (1 + 0.25) = 160 \times 1.25 = 200 \text{ frames per second}

Increasing a value by

25\%

is equivalent to multiplying the original value by

1.25

Calculate total frames recorded in

14

seconds at the new rate.

200 \text{ frames per second} \times 14 \text{ seconds} = 2,800 \text{ frames}

Multiplying the new rate by the given duration yields the total frame count.

Key Concept

Unit rates and percentage adjustment in rates

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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