Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Two workers have different pay scales. Worker A receives \(\$ 50\) for any day worked plus \(\$ 15\) per hour. Worker \(B\) receives \(\$ 27\) per hour. Both workers may work for a fraction of an hour and be paid in proportion to their respective hourly rates. If worker A arrives at 9: 21 a.m. and receives the \(\$ 50\) upon arrival and Worker \(\mathrm{B}\) arrives at 10: 09 a.m. assuming both work continuously, at what time would their earnings be identical? a. \(11: 09 \mathrm{a.m}.\) b. \(12: 01 \mathrm{p.m}.\) c. \(2: 31 \mathrm{p.m}.\) d. \(3: 19 \mathrm{p.m}.\) e. \(3: 36 \mathrm{p.m}.\)

Short Answer

Expert verified
3:19 p.m.

Step by step solution

01

- Define Earnings for Worker A

Worker A earns a base pay of \(\$50\) plus \(\$15\) per hour worked. Let \(t\) be the number of hours worked after arriving at 9:21 a.m. Hence, Worker A's earnings as a function of time \(t\) in hours can be written as: \[ E_A = 50 + 15t \]
02

- Define Earnings for Worker B

Worker B earns \(\$27\) per hour worked. Worker B arrives at 10:09 a.m., which is 48 minutes or 0.8 hours after Worker A. Let \(t\) be the number of hours Worker A has worked. Worker B's earnings as a function of time \(t\) can be written as: \[ E_B = 27(t - 0.8) \] because Worker B starts working 0.8 hours after Worker A.
03

- Set Earnings Equal

To find the time when their earnings are identical, set \(E_A = E_B\): \[ 50 + 15t = 27(t - 0.8) \]
04

- Solve for t

Solve the equation \( 50 + 15t = 27(t - 0.8) \): \[50 + 15t = 27t - 21.6\] \[\Rightarrow 50 + 15t = 27t - 21.6\] \[\Rightarrow 50 + 21.6 = 27t - 15t\] \[\Rightarrow 71.6 = 12t\] \[\Rightarrow t = \frac{71.6}{12} \approx 5.967\] Therefore, Worker A has worked for approximately 5.967 hours since 9:21 a.m.
05

- Convert Hours to Time

Convert 5.967 hours to hours and minutes: \[ 0.967 \times 60 \approx 58 \] minutes. Thus, Worker A has worked for 5 hours and 58 minutes. Add this time to Worker A's start time of 9:21 a.m.: \[ 9:21 \text{ a.m.} + 5:58 \text{ hours} = 3:19 \text{ p.m.}\] Therefore, the time when both workers' earnings are identical is 3:19 p.m.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Earnings Calculation
Understanding how to calculate earnings is crucial in many real-life scenarios, especially when dealing with pay rates that involve both a base rate and an hourly wage. In this problem, Worker A has a base pay of \( \$50 \) plus an additional \( \$15 \) per hour worked. Worker B, on the other hand, earns \( \$27 \) per hour with no base pay. To find the total earnings for each worker, you need to account for both parts in Worker A's case and just the hourly rate for Worker B. Understanding and being able to set up these calculations correctly can significantly help when solving complex work and pay rate problems.
Work Rate
The concept of work rate deals with how much work is done or how much money is earned within a given period, usually per hour. In this exercise, Worker A works from 9:21 a.m. and earns \( \$15 \) per hour after the initial \( \$50 \) base pay. Worker B starts working 48 minutes later, at 10:09 a.m., earning \( \$27 \) per hour. Calculating the work rate can involve different start times and adjusting the formulas accordingly to integrate the delayed starting time. This helps determine who earns more over the same period and can show the exact time when their earnings match.
Linear Equations
Linear equations are used to represent relationships between quantities. They are especially useful in problems involving rates and time. In this example, we set the earnings of Worker A equal to the earnings of Worker B to find the specific point in time when both workers earn the same amount. The equation \(50 + 15t = 27(t - 0.8)\) is at the heart of this calculation. Solving this linear equation involves combining like terms and isolating the variable \(t\). Learning how to manipulate and solve these equations is fundamental in algebra and applies directly to financial calculations involving salaries and hours worked.
Time Conversion
Converting time from hours and minutes to a decimal format and vice versa is essential in solving problems with different starting points and work durations. In this case, we need to convert 48 minutes to its decimal form (0.8 hours) and later, the calculated 5.967 hours back into hours and minutes. Understanding these conversions allows students to accurately add or subtract times, ensuring the final answer is precise. For instance, converting 0.967 hours to minutes involves multiplying by 60, resulting in approximately 58 minutes, which is then added to the initial time of 9:21 a.m. to find the final time of 3:19 p.m.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Set \(X\) consists of at least 2 members and is a set of consecutive odd integers with an average (arithmetic mean) of 37. Set \(Y\) consists of at least 10 members and is also a set of consecutive odd integers with an average (arithmetic mean) of 37. Set \(Z\) consists of all of the members of both set \(X\) and set \(Y\). Which of the following statements must be true? I. The standard deviation of set \(Z\) is not equal to the standard deviation of set \(X\). II. The standard deviation of set \(Z\) is equal to the standard deviation of set \(Y\). III. The average (arithmetic mean) of set \(Z\) is 37. a. I only b. II only c. III only d. I and III e. II and III

When the cube of a non-zero number \(y\) is subtracted from \(35,\) the result is equal to the result of dividing 216 by the cube of that number \(y .\) What is the sum of all the possible values of \(y ?\) a. \(\frac{5}{2}\) b. 5 c. 6 d. 10 e. 12

There are 816 students in enrolled at a certain high school. Each of these students is taking at least one of the subjects economics, geography, and biology. The sum of the number of students taking exactly one of these subjects and the number of students taking all 3 of these subjects is 5 times the number of students taking exactly 2 of these subjects. The ratio of the number of students taking only the two subjects economics and geography to the number of students taking only the two subjects economics and biology to the number of students taking only the two subjects geography and biology is \(3: 6: 8 .\) How many of the students enrolled at this high school are taking only the two subjects geography and biology? a. 35 b. 42 c. 64 d. 136 e. 240

For all values of \(x, y,\) and \(z, x \diamond y \diamond z=x^{2}(y-1)(z+2)\). If \(a<0,\) which of the following shows \(R, S,\) and \(T\) arranged in order from least to greatest? \(R: 1 \diamond a \diamond 3\) \(S: 3 \diamond a \diamond 1\) \(T: a \diamond 3 \diamond 1\) a. \(R, S, T\) b. \(T, S, R\) c. \(R, T, S\) d. \(T, R, S\) e. \(S, R, T\)

If \(\frac{61^{2}-1}{h}\) is an integer, then \(h\) could be divisible by each of the following EXCEPT: a. 8 b. 12 c. 15 d. 18 e. 31

See all solutions

Recommended explanations on English Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free