John takes 15 hours to complete a certain job, while Bill takes only 6

Its Option B here.

John can complete the work in 15 hours so the amount of work completed in hour= 1/15

Bill can complete the work in 6 hours, so the amount of work complete in one hour= 1/6

Add above two,

1/15+ 1/6 = 7/30.

Now Test the answer choices,

Option 1: 7/30+ 1/ X = 2/5 => X= 6 hours.

Option 2: 7/30 + 1/X= 4/11 (x=Around 7. 5 ish...)

Option 3: 7/30 + 1/x = 3/10 (X is 15)

OPTION 4 and 5 will be definitely greater than 15. Hence Option B correct.

(As bills work will be between 6 and 15)

Set up a rate/time/work table and plug in 30 as for the "work":

John 2 15 30
Bill 5 6 30
Steve >2, <5 ?

Compound R X 30

Plug in the answer choices in the function of the compound rate. If you plug in A which is 2.5 hours, Steves Rate would be 5 which is not smaller than Bills rate. Answer Choice B fits, making Steve's Rate 3.9.

AC B.

Hello,
We can answer this by obtaining values for the extremes as per the stated conditions. Correct answer will fall in between the extremes. It is told that Steve is faster than John i.e he takes less than 15 hours and greater than Bill i.e. he takes more than 6 hours.

Step 1 : Let's calculate one extreme by assuming Steve took the same amount as John to complete the work. The total time taken by three then will be 1/15+1/15+1/6 ( rates respective for John, Steve and Bill) which equals 3 hours 20 mins. (Applied RT=W)

Step 2 : Let's calculate other extreme by assuming Steve took the same amount as Bill to complete the work. The total time taken by three then will be 1/15+1/6+1/6 (rates respective for John, Steve and Bill) which equals 2 hours 30 mins. (Applied RT=W)

The correct answer shall fall in between these two values and looking at answer choices we see that only option B is the value that does so.

Hence correct answer is B

I assumed S = 1/10.. 1/15 + 1/6 + 1/10 = 3/9 j/h ... = 9/3h/j = 3h

Question is..which could be the time ? Hence, why is C incorrect ?

It is given in the question statement that Steve takes less time then John. They take exactly 3hrs20mins if Steve takes exactly the same amount of time as John, but we know that it is not the case. So the total time taken should be less than 3hrs 20 mins and more than 2hrs 30mins as these are the two extreme values obtained as per the statement. Hope I am clear ?

hi,
you have assumed 1/10 correctly but solved it wrongly..
\(\frac{1}{10}+\frac{1}{15}+\frac{1}{6}=\frac{(3+2+5)}{30}=\frac{10}{30}=\frac{1}{3}\)
so ans is 3 hrs and not 3 hrs 20 min...
if 3 hrs was a choice it would have been correct
hope it is clear now

we can find two extreme ends, which are just out of the range

1) lower end... j=15h, b=6h and j=15h
all three will take1(1/15+1/15+1/6)= 2h 30 min
2) higher end j=15h, b=6h and j=6h
all three will take1(1/15+1/6+1/6)= 3h 20 min..

only B is within this range
ans B

ye..already edited! Thanks!

damn..I chose a very long way to solve it..thus..spending a lot of time
since S works faster than J, but slower than B, we can take extremities
S = 14
S = 7

by solving this, we see that the time is between 2h30+m and 3h16m
the only answer choice that falls between this interval is B.

John and Bill complete the work in 90/21 hours; if Steve joins them, the time taken to complete the job will be less than this time.
Steve's time taken is between 15 hours and 6 hours.
Find the limiting value for 90/21 and 15 and 90/21 and 6; that gives 3 hours 20 m and 2 hours and 30 min
That implies the answer has to be between these limits.

Assume the units of work to be 90

Since John takes 15 hours to finish the work, the rate of John's work is 6 units/hour
Similarly, Bill take 6 hours to finish the work, the rate of Bill's work is 15 units/hour

Since it has been given that the rate of Steve is greater than John and lesser than Bill,
the range of Steve's rate is between 6 units/hour and 15 units/hour
Hence the range of the time take to complete the work is between
\(\frac{90}{(6+6+15)}\) = 3.33 hours(3 hour, 20 mins) and \(\frac{90}{(6+15+15)}\) = 2.5 hours(2 hour, 30 mins)

The only value within this range is 2 hour, 45 mins(Option B)

hi, could you plz explain how 2/5, 4/11 and 3/10 came?

Let the total work to be done is 30
Rate of John and Bill is 2 and 5 respectively.
Now Rate of Steve is >2 and <5
So if rate is 2
Together they do 2+5+2 = 9 work / hour
So to complete 30 work they will take \(\frac{30}{9}\) = 3 hrs 20 mins
If rate of work is 5
Together they do 2+5+5=12 work / hour
So to complete 30 work they will take \(\frac{30}{12}\) = 2 hrs 30 mins
Thus answer should be between 2 hrs 30 mins and 3 hrs 20 mins
Only option is Option B

The idea is to find two extremes as implied in the question stem. What if Steve's rate was equal to John. In that case, the time taken would be:
(1/15 + 1/15 + 1/6) x t = w.
On solving, we get t = 3 hours 20mins.

Similarly, what if Steve's rate was equal to Bill. In that case, the time taken would be:
(1/15 + 1/6 + 1/6) x t = w.
On solving, we get t = 2 hours 30mins.

The only option in the middle of this range is Answer choice B. Hence the answer.

hello:chetan2u
i used :

1/j+1/b+1/s=1/r so the range will be
1- 1/15 +1/15 +1/6 =1/r .....> 9/30=1/r so r = 30/9 =3.33 (3:20min)
2- 1/15+1/6+1/6=1/r ......> 12/30=1/r so r = 30/12= 2.5( 2:30min)
the correct answer is between (2:30 _ 3:20)
(B) is this correct ? thank u

Let's first see what happens if Steven works as fast as possible.
Since Bill can complete the job in 6 hours, Steven must complete the job in a little more than 6 hours.
For example, we COULD see what happens if Steven takes 6.000000000000001 hours to complete the job.
Unfortunately, 6.000000000000001 is an awful number to work with.
So, for convenience sake, let's just see what happens if it takes Steven 6 hours to complete the job

----ASIDE-------
For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
---------------------
Let’s use these rules to solve the question. . . .

From Rule #1, we can conclude that:
- In ONE hour, John completes 1/15 of the job
- In ONE hour, Bill completes 1/6 of the job
- In ONE hour, Steven completes 1/6 of the job
So, COMBINED, the amount of the job completed after ONE hour = 1/15 + 1/6 + 1/6
= 2/30 + 5/30 + 5/30
= 12/30
= 2/5

Rule #2 tells us that, the total time to complete the job = 5/2 hours
In other words, when Steven works as FAST as possible, it takes the 3 men 5/2 hours to complete the job.
Of course, this calculation is based on Steven working at the SAME SPEED as Bill.
Since Steven is supposed to work SLOWER than Bill, the time it takes the 3 men to complete the job must be GREATER than 5/2 hours (aka 2 hours and 30 minutes)

IMPORTANT: We know that the correct answer must be GREATER than 2 hours and 30 minutes. So, we can eliminate answer choice A because it is too small.
We also know that, IF we were to also use Steven's SLOWEST work speed to calculate the upper limit for the time it takes all 3 men to complete the job, we'd be able to eliminate 3 more answer choices because they're too big.
Based on this, we should see that we can automatically eliminate the 3 biggest remaining answer choices (C, D, E), which leaves us with B

Answer: B

Cheers,
Brent

John’s rate is 1/15, and Bill’s rate is 1/6.

If Steve is as fast as John, his rate is 1/15, and the combined rate would be 1/15 + 1/6 + 1/15 = 2/30 + 5/30 + 2/30 = 9/30 = 3/10. Therefore, it would take the three men 1/(3/10) = 10/3 = 3 ⅓ = 3 hours and 20 minutes to complete the job.

On the other hand, if Steve is as fast as Bill, his rate is 1/6, and the combined rate would be 1/15 + 1/6 + 1/6 = 2/30 + 5/30 + 5/30 = 12/30 = 2/5. Therefore, it would take the three men 1/(2/5) = 5/2 = 2 1/2 = 2 hours and 30 minutes to complete the job.

Since Steve is faster than John but slower than Bill, it will take them between 2 hours and 30 minutes and 3 hours and 20 minutes to complete the job. We see that of all the answer choices, only choice B, 2 hours and 45 minutes, satisfies the criteria.

Answer: B