Two workers have different pay scales. Worker A receives $50 for any

Question

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 B arrives at 10:09 a.m., assuming both work continuously, at what time would their earnings be identical?

(A) 11:09 a.m.
(B) 12:01 p.m.
(C) 2:31 p.m.
(D) 3:19 p.m.
(E) 3:36 p.m.

Are You Up For the Challenge: 700 Level Questions

(A) 11:09 a.m.
(B) 12:01 p.m.
(C) 2:31 p.m.
(D) 3:19 p.m.
(E) 3:36 p.m.

Are You Up For the Challenge: 700 Level Questions

Nidzo · Accepted Answer

A  starts at 09:21 and works for 48 minutes before  B  arrives. In that time  A  earns  (\frac{48}{60}*15) + 50 = 62 .

As  A  is $62 ahead already, the relative rate of  A&B  will be  27 - 15 = 12  dollars an hour.

They will therefore have the same earnings after:  \frac{62}{12} = 5\frac{1}{6}  hours, or 5 hours and 10 minutes.

Adding 5 hours and 10 minutes to 10:09 will make it 3:19PM.

Answer D

RahulJain293 · Answer

Solution:

Given Data:
A - 50$ + 15$ each hour
B - only 27$ per hour (no starting $)

A starts at 9:21 AM. Let's calculate what happens at 10:21 AM

@10:21 AM -

A has 50+15 = 65$

At this point, B is working for 12 Minutes (as it starts at 10:09).
In 60 minutes, B makes 27$. Hence, in 12 minutes, B makes 27/5 = 5.4$

Therefore, at 10:21AM
A has 65$
B has 5.4$

Now since B has quite a lot to catchup, let's try with what happens in 5 hours (ie 3:21 looking at options)

Hence we add 5*15 = 75$ to A
And we add 5*27 = 135$ to B

Hence at 3:21 we have
A with 65+75 = 140$
B with 5.4+135 = 140.4$

Now, since they are pretty close, the Option D, which is 2 minutes less should make both A & B equal.

Hence D

Purnank · Answer

Equation way,
First converting rates into per min basis 
For A it will be 50 fixed + additional 15/60 = 1/4 per min and for B 27/60 = 9/20 per min
A came 48 mins before B,
assuming they work for n mins after B came.
 50 + \frac{(n+48)}{4} = \frac{9n}{20} 
Solve for n,
we get n = 310 min
Add this to time of B,
  Answer is D.

AndyRugger · Answer

I set up an inequality where their earnings would equal.

50 + 15*Total Time = 0 + 27*(Total Time - Time Delta), where Time Delta = 10:09 - 9:21 = 5/6 hrs.

Make a few easy round offs for easy multiplication and you land on the answer in less than 2 minutes of algebra manipulation.

This way isn't the fastest, but so long as we keep your time variables in order, it's the most straightforward.

Two workers have different pay scales. Worker A receives $50 for any

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Two workers have different pay scales. Worker A receives $50 for any

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