Rate Problem 4

[phoenix9801]

Hi, If someone help me on rate problem please I would greatly Appropriate it. I just want to ensure I have done them correctly. Thanks


Jack made his first x dollars at an average rate of 50 dollars per hour and the remaining amount at an average rate of 60 dollars per hour. How long did it take Jack to make the first x dollars if he worked for a total of 10 hours averaging 53 dollars per hour?

A) 4.5
B) 6
C) 7
D) 9
E) 9.25

[GMATGuruNY]

Hi, If someone help me on rate problem please I would greatly Appropriate it. I just want to ensure I have done them correctly. Thanks


Jack made his first x dollars at an average rate of 50 dollars per hour and the remaining amount at an average rate of 60 dollars per hour. How long did it take Jack to make the first x dollars if he worked for a total of 10 hours averaging 53 dollars per hour?

A) 4.5
B) 6
C) 7
D) 9
E) 9.25

Total amount earned = 10*53 = 530.

We can plug in the answers, which represent the time worked at a rate of 50 dollars per hour.

Answer choice C: 7 hours at 50 dollars per hour, implying 3 hours at 60 dollars per hour
Total earned = 7*50 + 3*60 = 350+180 = 530.
Success!

The correct answer is C.

[GMAT Kolaveri]

Solving using Alligations method: It takes only few seconds to solve
A1------------------------------- A2
50------------------------------60

--------------- Aw
---------------- 53

A2-Aw -------------------------- Aw-A1
60-53--------------------------- 53-50
7------------------------ 3

[eagleeye]

Here's a traditional math reply. Its a simple equation to solve.

let the time required to make first x dollars be t (when the earning was 50$/hr) and then the remaining time is (10-t) (working at 60$ per hour).

Then we have 50*t + 60* (10-t) = 53*10 => 50t+600-60t=530, hence 10t = 70 or t = 7 hours.

Let me know if this helps