Work/Rate problem

[BTGmoderatorRO]

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P's hourly wage is how many dollars greater than candidate Q's hourly wage?
A) $10
B) $15
C) $20
D) $25
E) $30
OA is a

Can option D truly be the correct answer or am I wrong somewhere in my calculation? I am really confused here. Can any expert help me out here?
Thanks

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Hi Roland2rule,

This question gives us a number of facts to work with:
1) The project pays 600 dollars in total.
2) Candidate P would be paid 50 percent more per hour than candidate Q would be paid.
3) Candidate Q would require 10 hours more than candidate P to do the job.

With this information, we can create two equations and solve using "system Algebra." We're asked for the difference between Candidate P's hourly wage and candidate Q's hourly wage.

X = pay per hour
T = number of hours

Candidate P = ($1.5X)(T) = 600
Candidate Q = ($X)(T+10) = 600

(1.5)(X)(T) = 600
XT + 10X = 600

In the first equation, we can divide both sides by 1.5, which gives us:
XT = 600/1.5 = 400
We can then substitute this value into the second equation:
400 + 10X = 600
10X = 200
X = 20

Since X = $20, 1.5X = $30 and the difference is $10

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

P and Q are the only two applicants qualified for a short-term research project that pays 600 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P's hourly wage is how many dollars greater than candidate Q's hourly wage?
A) $10
B) $15
C) $20
D) $25
E) $30

We know that hourly wage = total paid/number of hours.

If we let h = the number of hours worked by P, then h + 10 = the number of hours worked by Q. Thus:

600/h = 1.5[600/(h+10)]

600/h = 900/(h + 10)

600(h + 10) = 900h

600h + 6000 = 900h

6000 = 300h

20 = h

Thus, P's hourly wage is 600/20 = $30 and Q's hourly wage is 600/30 = $20. Thus, P's hourly wage is 30 - 20 = 10 dollars greater than Q's hourly wage.

Answer: A