Distance/Rate and Work/Rate

Question 1

What is the Distance/Time formula?

Answer 1

D=RT

D: Distance (how far something has traveled)
R: Rate (The speed at which something is moving)
T: Time (The Duration for which the movement occurred)

Example: If you drive at rate (R) of 60 mph for a time (T) of 2 hours, the distance (D) you’ve covered is 60*2 = 120 miles.

Question 2

What is the Work/Rate Formula?

Answer 2

W=RT

W: Work (Usually represented as a complete job or task, often set to 1 unit for simplicity)
R: Rate (The portion of the job or task completed per unit of time, E.G, per hour)
T: Time (The duration taken to complete the work)

Example:

If a machine completes 1/4 of a task per hour (Rate) and works for 8 hours (Time), the total Work done is W = 1/4 * 8 = 2 units of the task

Question 3

How do you convert the time taken to complete a job into a ratio?

Answer 3

Conversion principle:

• The rate of work is the inverse of the time taken to complete the entire job.

Formula:

• If it takes T hours to complete a job, then the rate R is:

R=1/T

Example:

• If it takes 6 hours for a person to complete a job, then the rate is:

R=1/6

This means the person completes 1/6 of the job per hour.

Question 4

How do you determine the work rate when the work is not one complete unit?

Answer 4

Conversion Principle:

• When the work W is not one complete unit, use the W=RT formula to determine the rate.

Formula:

• Given W as the fraction of the job and t as the time taken:

R=W/T

Example:

If a person takes 6 hours to complete 2/3 of the job:

R=2/3 divided by 6 = 1/9

This means the person completes 1/9 of the job per hour.

Question 5

What is the formula to determine the combined work rate and time for two workers (or machines) working together?

Answer 5

Work Rate Formula:

1.- If worker A completes a job in X hours, their work rate is 1/X of the job per hour
2.- If worker B completes a job in Y hours, their work rate is 1/Y of the job per hour

Combined Work Rate:

Combined Rate = 1/X + 1/Y

Time for combined Work:

Time = 1 / Combined Rate

Question 6

How is the rate structured in work problems?

Answer 6

Rate = Amount of work or change / unit of time

• Numerator (amount of work or change): Represents the quantity of work done or the amount of change that has occurred.
• Denominator (Unit of time): Represernts the time over which that work was done or change occurred.

*In work problems, always think of the rate as “How much work is done in one unit of time”

Question 7

Do 3 problem GPT - Rates & Hard Rates Problems

Answer 7

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