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If a rocket can travel x/5 miles every y seconds, how many miles can i

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If a rocket can travel x/5 miles every y seconds, how many miles can i  [#permalink]

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New post Updated on: 12 Jul 2018, 21:09
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Question Stats:

68% (01:02) correct 32% (01:18) wrong based on 31 sessions

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If a rocket can travel \(\frac{x}{5}\) miles every y seconds, how many miles can it travel in z minutes?


A. \(\frac{xy}{5z}\)

B. \(\frac{xz}{5y}\)

C. \(\frac{xyz}{6}\)

D. \(\frac{12xy}{z}\)

E. \(\frac{12xz}{y}\)

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Originally posted by carcass on 12 Jul 2018, 09:38.
Last edited by Bunuel on 12 Jul 2018, 21:09, edited 1 time in total.
Renamed the topic.
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Re: If a rocket can travel x/5 miles every y seconds, how many miles can i  [#permalink]

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New post 12 Jul 2018, 09:51
1
First we need to convert the first rate in minutes. If x/5 miles are traveled in y seconds, we need to divide this distance by y to find the distance traveled in 1 second.

distance traveled in 1 second = x/5y

Then let's find the distance traveled in 1 minute, by multiplying the previous distance by 60.

distance traveled in 1 minute: 60x/5y

Finally we need to multiply this distance by z to find the distance traveled in z minutes:

distance traveled in z minutes: 60xz/5y.

Reduce the fraction: 12xz/y.

Answer E.
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Re: If a rocket can travel x/5 miles every y seconds, how many miles can i  [#permalink]

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New post 12 Jul 2018, 10:16
2
carcass wrote:
If a rocket can travel \(\frac{x}{5}\) miles every y seconds, how many miles can it travel in z minutes?

A. \(\frac{xy}{5z}\)

B. \(\frac{xz}{5y}\)

C. \(\frac{xyz}{6}\)

D. \(\frac{12xy}{z}\)

E. \(\frac{12xz}{y}\)



1) Algebraic method :-
\(\frac{x}{5}\) in y seconds
so \(\frac{x}{5y}\) in 1 second
or \(\frac{60x}{5y}=\frac{12x}{y}\) in 60 seconds or 1 minute
therefore in z minutes \(\frac{12xz}{y}\)

2) substitution
take x = 5, so that 5/5 becomes 1
take y = 60 seconds, so that it becomes 1 minute
take z = 1
so 5/5 = 1 in 60 seconds or 1 minute which is same as z minute

substitute in choices and you should get 1 as the answer..
A. \(\frac{xy}{5z}......\frac{5*60}{5*1}\neq{1}\)

B. \(\frac{xz}{5y}..........\frac{5*1}{5*60}\neq{1}\)

C. \(\frac{xyz}{6}...........\frac{5*60*1}{6}\neq{1}\)

D. \(\frac{12xy}{z}.........\frac{12*5*60}{1}\neq{1}\)

E. \(\frac{12xz}{y}..........\frac{12*5*1}{60}=1\)...Answer


E
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Re: If a rocket can travel x/5 miles every y seconds, how many miles can i  [#permalink]

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New post 12 Jul 2018, 12:58
1
carcass wrote:
If a rocket can travel \(\frac{x}{5}\) miles every y seconds, how many miles can it travel in z minutes?

A. \(\frac{xy}{5z}\)

B. \(\frac{xz}{5y}\)

C. \(\frac{xyz}{6}\)

D. \(\frac{12xy}{z}\)

E. \(\frac{12xz}{y}\)



In y sec rocket can travel \(\frac{x}{5}\) miles

In 1 sec rocket can travel (x/5) /y miles

In 60 sec rocket can travel (x/5)*60 / y miles

So, In 1 min ( 60 sec) rocket can travel\(\frac{12x}{y}\) miles.

If in 1 min. rocket can travel \(\frac{12x}{y}\) miles , in z min it will travel \(\frac{12xz}{y}\) miles.


Thus the best answer is E.
Re: If a rocket can travel x/5 miles every y seconds, how many miles can i &nbs [#permalink] 12 Jul 2018, 12:58
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