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Updated on: 06 Mar 2026, 19:38
Originally posted by MartyMurray on 07 Sep 2025, 07:20.
Last edited by MartyMurray on 06 Mar 2026, 19:38, edited 2 times in total.
Last edited by MartyMurray on 06 Mar 2026, 19:38, edited 2 times in total.
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D
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Difficulty:
95%
(hard)
Question Stats:
50% (02:58) correct
50%
(02:37)
wrong
based on 135
sessions
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Working at his normal constant rate, John fills a certain type of order in 3t whereas Mary, working at her normal constant rate, fills the same type of order in t. If at the same time each of them begins to fill an order at his or her normal constant rate, after how much time has passed in terms of t will Mary have remaining 1/3 the work to complete her order that John has remaining to complete his?
(A) \(\frac{t}{3}\)
(B) \(\frac{t}{2}\)
(C) \(\frac{2t}{3}\)
(D) \(\frac{3t}{4}\)
(E) \(t\)
Source: Marty Murray Coaching
(A) \(\frac{t}{3}\)
(B) \(\frac{t}{2}\)
(C) \(\frac{2t}{3}\)
(D) \(\frac{3t}{4}\)
(E) \(t\)
Source: Marty Murray Coaching
07 Sep 2025, 07:38
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Working at his normal constant rate, John fills a certain type of order in 3t whereas Mary, working at her normal constant rate, fills the same type of order in t. If at the same time each of them begins to fill an order at his or her normal constant rate, after how much time has passed in terms of t will Mary have remaining 1/3 the work to complete her order that John has remaining to complete his?
John's rate: \(\frac{1}{3t}\)
Mary's rate: \(\frac{1}{t}\)
Amount of time passed: \(x\)
Amount of work John completes in \(x\) time: \(\frac{x}{3t}\)
Amount of work John has remaining after \(x\) time has passed: \(1 - \frac{x}{3t}\)
Amount of work Mary completes in \(x\) time: \(\frac{x}{t}\)
Amount of work Mary has remaining after \(x\) time has passed: \(1 - \frac{x}{t}\)
after how much time has passed in terms of t will Mary have remaining 1/3 the work ... that John has remaining
\(\frac{1}{3}(1 - \frac{x}{3t}) = 1 - \frac{x}{t}\)
\(1 - \frac{x}{3t} = 3 - \frac{3x}{t}\)
\(3t - x = 9t - 9x\)
\(8x = 6t\)
\(x = \frac{3t}{4}\)
(A) \(\frac{t}{3}\)
(B) \(\frac{t}{2}\)
(C) \(\frac{2t}{3}\)
(D) \(\frac{3t}{4}\)
(E) \(t\)
Correct answer: D
John's rate: \(\frac{1}{3t}\)
Mary's rate: \(\frac{1}{t}\)
Amount of time passed: \(x\)
Amount of work John completes in \(x\) time: \(\frac{x}{3t}\)
Amount of work John has remaining after \(x\) time has passed: \(1 - \frac{x}{3t}\)
Amount of work Mary completes in \(x\) time: \(\frac{x}{t}\)
Amount of work Mary has remaining after \(x\) time has passed: \(1 - \frac{x}{t}\)
after how much time has passed in terms of t will Mary have remaining 1/3 the work ... that John has remaining
\(\frac{1}{3}(1 - \frac{x}{3t}) = 1 - \frac{x}{t}\)
\(1 - \frac{x}{3t} = 3 - \frac{3x}{t}\)
\(3t - x = 9t - 9x\)
\(8x = 6t\)
\(x = \frac{3t}{4}\)
(A) \(\frac{t}{3}\)
(B) \(\frac{t}{2}\)
(C) \(\frac{2t}{3}\)
(D) \(\frac{3t}{4}\)
(E) \(t\)
Correct answer: D
PocusFocus
11 Sep 2025, 19:56
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As usual, nice problem Marty, it took me a while but did it correctly, here my solution:
Let's assume that work the amount of work is 3t
And (t') will be our incognita, after t' Jhon will advanced t' of work and Mary 3t' of work , now
Let's say that 3a is the amount of work remaining for John, so:
t' + 3a = 3t' + a --> a = t' --> replacing a = t' --> total work = 4t' = 3t, t' = 3t/4
Let's assume that work the amount of work is 3t
| Time | Work | Rate | |
| Jhon | 3t | 3t | 1 |
| Mary | t | 3t | 3 |
And (t') will be our incognita, after t' Jhon will advanced t' of work and Mary 3t' of work , now
Let's say that 3a is the amount of work remaining for John, so:
t' + 3a = 3t' + a --> a = t' --> replacing a = t' --> total work = 4t' = 3t, t' = 3t/4
