Question: Lawn Mowers

Comment on Lawn Mowers

Brent,

Could you help me with the exercises 140, 324, 333 and 337 of the OG 2017.

Thank you.
Pedro

Brent,

Thank you for your help. I have two more doubts regarding two other exercises of OG17: Questions #203 and #377, could you help me please?

Thanks,
Pedro
gmat-admin's picture

Glad to help, Pedro!

QUESTION #203

That's a VERY tricky question.

ceilidh.erickson provides a nice solution here: http://www.beatthegmat.com/plz-explain-official-guide-ps-q-178-t281640.html

Her response is the 2nd one listed in the thread.

If you have any questions about her solution, let me know.

NOTE: This is not a common question type on the GMAT, and I think most students will not see one on test day.

-------------------------------------
QUESTION #377
My step-by-step solution can be found here: https://gmatclub.com/forum/in-planning-for-a-trip-joan-estimated-both-th...

Cheers,
Brent

Thank you very much, Brent!

Cheers,
Pedro

Hey Brent. I solved it like this:

B&E can mow 1 lawn in 2 hours, so in 1 hour they can mow 1/2 lawn.
K can mow 1 lawn in 3 hours, so in 1 hour he can mow 1/3 lawn.

Combined they can mow (1/2)(3/3) + (1/3)(2/2) = 3/6 + 2/6 = 5/6

So in 60 minutes they mow 5/6 lawn. 60/5 = 12 minutes. They spend 12 minutes per "part", and they are missing 1 part, so therefore the time spent will be 60 minutes plus 12 minutes for that last part, which equals 72 minutes total.

Is this a valid way to solve it?
gmat-admin's picture

Yes, that is a valid approach. However, we can save some time by applying the following rule:

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.

So, in this question, they can mow 5/6 of the job in ONE HOUR. So, it will take them 6/5 hours to mow the entire lawn.

Cheers,
Brent

Hi Brent,

Can you please answer this question:

At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

(A) 3/25
(B) 11/36
(C) 7/12
(D) 2/3
(E) 25/36
gmat-admin's picture

Dear Brent,

could you help me with the following problem:

Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

A. 4
B. 6
C. 8
D. 10
E. 12

In the solution, there is always t-2 and not t+2 in the equation.
Why can't i solve it with t+2 ?
Moreover, how can i easily solve the equation: 5t^2-34t+24=0 ?


Thanks a lot!
gmat-admin's picture

We can use EITHER t+2 OR t-2, depending on how we assign our variables.

GIVEN: machine X takes 2 days longer to produce w widgets than machines Y.

If we let t = time for machine X to produce w widgets, then t-2 = time for machine Y to produce w widgets.

If we let t = time for machine Y to produce w widgets, then t+2 = time for machine X to produce w widgets.

In my solution, I use t and t+2: https://gmatclub.com/forum/running-at-their-respective-constant-rates-ma...

Solving 5t² - 34t + 24 = 0 is a bit of a pain.
IMPORTANT: Your equation is a little off. It should be 5t² - 14t - 24 = 0

We know that the first two terms must have a product of 5t²
There's only one way to accomplish this: 5t times t
So, we can write: 5t² - 14t - 24 = (5t +/- ?)(t +/- ?)

We know that the last two terms must have a product of -24
So, one value must be POSITIVE and one must be NEGATIVE

At this point, we need to test some of our options.

For example, does (5t - 1)(t + 24) = 5t² - 14t - 24?
NO. Keep trying.

Does (5t - 24)(t + 1) = 5t² - 14t - 24?
NO. Keep trying.
.
.
.

Does (5t + 6)(t - 4) = 5t² - 14t - 24?
YES!

So, we know that: 5t² - 14t - 24 = 0
...becomes (5t + 6)(t - 4) = 0

Does that help?

Cheers,
Brent

I feel like I didn't entirely get the relationships between O and RT, that's why im constantly stucking. although I do know O/RT, but cannot apply them properly when tacking questions
gmat-admin's picture

Perhaps it'll help if I list all three equations:
O = RT
R = O/T
T = O/R

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