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Marcus can build t tree houses in h houses. How many tree houses can h

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Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 04 Apr 2019, 03:27
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Marcus can build t tree houses in h hours. How many tree houses can he produce in m minutes and s seconds?

a. (60mt+s)/3600h

b. (60m+s)/3600h

c. t(60m+s)/3600h

d. (60mt)/3600h

e. t(m+s)/3600h

Thanks!
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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 04 Apr 2019, 09:19
Please explain the solution.

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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 05 Apr 2019, 22:44
chetan2u Bunuel VeritasKarishma Gladiator59

Please advise for units conversion and how to proceed from knowing initial rate as
t/h hrs? Does t remain constant when we add m mins and s secs?
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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 05 Apr 2019, 23:31
2
Aviv29 wrote:
Marcus can build t tree houses in h hours. How many tree houses can he produce in m minutes and s seconds?

a. (60mt+s)/3600h

b. (60m+s)/3600h

c. t(60m+s)/3600h

d. (60mt)/3600h

e. t(m+s)/3600h

Thanks!


t houses in h hours
t houses in 60h mins
In m mins, (t/60h)*m

t houses in h hours
t houses in 3600h secs
In s secs, (t/3600h)*s

No of houses built in m mins and s secs = (t/60h)*m + (t/3600h)*s houses

= (mt60 + st)/3600h houses

= t(60m + s) / 3600h houses

Answer (C)


Alternatively, plug in values. Say he builds 10 houses (t = 10) in 1 hr (h = 1).
He builds 10 houses in 59 mins (m = 59), 60 secs (s = 60).

Now just plug in these values to see which option gives you 10.
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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 06 Apr 2019, 00:02
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adkikani wrote:
chetan2u Bunuel VeritasKarishma Gladiator59

Please advise for units conversion and how to proceed from knowing initial rate as
t/h hrs? Does t remain constant when we add m mins and s secs?


My two cents

t houses in h hours =h*60*60 seconds

so per second house constructed = t/(h*3600 )

now

m minute = m*60 seconds

so total time = 60m+s seconds

house constructed = per second house constructed* total time in seconds

(60m+s)t/(h*3600)


IMO C


award kudos if helpful

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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 06 Apr 2019, 00:05
1
Aviv29 wrote:
Marcus can build t tree houses in h hours. How many tree houses can he produce in m minutes and s seconds?

a. (60mt+s)/3600h

b. (60m+s)/3600h

c. t(60m+s)/3600h

d. (60mt)/3600h

e. t(m+s)/3600h

Thanks!


CONCEPT: \(\frac{(Machine_Power * Time)}{Work} = Constant\)

i.e. \(\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}\)

h hours = 3600*h seconds and m minutes and s seconds = 60m+s seconds

i.e. \(\frac{(M * h*3600)}{t} = \frac{(M * (60m+s))}{W_2}\)

i.e. W_2 = (60m+s)*t/3600h

Answer: Option C

I hope this helps!!!
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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 06 Apr 2019, 04:23
Aviv29 wrote:
Marcus can build t tree houses in h hours. How many tree houses can he produce in m minutes and s seconds?

a. (60mt+s)/3600h

b. (60m+s)/3600h

c. t(60m+s)/3600h

d. (60mt)/3600h

e. t(m+s)/3600h

Thanks!


m minutes and s seconds in hours will be
m/60 + s/3600
we can say 1 h = 60m+s/3600

so total houses built in 1 hr ; t/h
or say

t*(60m+s)/3600h

IMO C
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Re: Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 06 Apr 2019, 04:48
in h hour houses built = t
in 1 houses built = t/h
in m/60 houses built = (t/h)*(m/60) Eq 1
in s/3600 houses built = (t/h)*(s/3600) Eq 2
Addin Eq 1 & 2 gives us
t(60m+s)/3600h i.e C
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Marcus can build t tree houses in h houses. How many tree houses can h  [#permalink]

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New post 06 Apr 2019, 05:25
1
Aviv29 wrote:
Marcus can build t tree houses in h hours. How many tree houses can he produce in m minutes and s seconds?

a. (60mt+s)/3600h

b. (60m+s)/3600h

c. t(60m+s)/3600h

d. (60mt)/3600h

e. t(m+s)/3600h

Thanks!



Rate of Marcus =\(\frac{t}{h}\)

Rate of Marcus = t/3600 (Rate per second)

\(Work = W\)

\(Time =\) \(m\) minutes +\(s\) seconds

\(Time =\) \(60m + s\) (minutes converted to seconds)

We know,

\(Work = Rate * Time\)

\(Work =\) \(\frac{t}{h} (60m + s)\)

\(Work =\) \(\frac{t}{3600}(60m+s)\)

C

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Marcus can build t tree houses in h houses. How many tree houses can h   [#permalink] 06 Apr 2019, 05:25
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