A laboratory dispensing pump releases a liquid solution at a constant rate of 0.75\text{ d… — SAT

A laboratory dispensing pump releases a liquid solution at a constant rate of $0.75\text{ deciliters per minute}$ . If $1\text{ deciliter} = 100\text{ milliliters}$ , what is the pump's dispensing rate, in milliliters per second?

Answer: 1.25 milliliters per second

Answer

The correct answer is 1.25. The pump dispenses 1.25 milliliters per second.

To find the dispensing rate in milliliters per second, we first convert the volume from deciliters to milliliters. Multiplying

0.75\text{ deciliters}

100\text{ milliliters per deciliter}

gives

75\text{ milliliters per minute}

. Next, to convert minutes to seconds, we divide the rate by

60

(since

1\text{ minute} = 60\text{ seconds}

), which yields

\frac{75}{60} = 1.25\text{ milliliters per second}

Step-by-Step Solution

Convert the dispensing rate from deciliters per minute to milliliters per minute using the conversion factor

1\text{ deciliter} = 100\text{ milliliters}

0.75\text{ deciliters/minute} \times 100\text{ milliliters/deciliter} = 75\text{ milliliters/minute}

This converts the volume unit from deciliters to milliliters.

Convert the rate from milliliters per minute to milliliters per second by dividing by

60

, since there are

60\text{ seconds}

1\text{ minute}

75\text{ milliliters/minute} \div 60\text{ seconds/minute} = 1.25\text{ milliliters/second}

This converts the time unit from minutes to seconds, yielding the final rate.

Key Concept

Unit Conversions

Alternative Method

Alternatively, you can convert the units in a single dimensional analysis step:

0.75 \text{ dL/min} \times \frac{100 \text{ mL}}{1 \text{ dL}} \times \frac{1 \text{ min}}{60 \text{ s}} = \frac{75}{60} \text{ mL/s} = 1.25 \text{ mL/s}

Estimated Time:1m 30s

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