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If Jim drives k miles in 50 minutes, how many minutes will it take him

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If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 15 Feb 2017, 06:04
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If Jim drives k miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. 500/k
B. k/500
C. 60k
D. 10k
E. 50/k

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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 15 Feb 2017, 06:07
1mile in 50/k min
so 10 mile in 500/k min

ans A

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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 15 Feb 2017, 09:20
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SajjadAhmad wrote:
If Jim drives k miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. 500/k
B. k/500
C. 60k
D. 10k
E. 50/k


We can also approach this question in terms of equivalent ratios

Jim drives k miles in 50 minutes
We're comparing miles traveled to minutes elapsed.
Jim travels k miles for every 50 minutes.
Our ratio is k miles/50 minutes

How many minutes will it take him to drive 10 miles, at the same rate?
So, our ratio is 10 miles/? minutes

So, our equation is: k/50 = 10/?
Cross multiply to get: (?)(k) = (50)(10)
Simplify: (?)(k) = 500
Solve for ? to get: ? = 500/k

Answer: A

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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 15 Feb 2017, 09:48
SajjadAhmad wrote:
If Jim drives k miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. 500/k
B. k/500
C. 60k
D. 10k
E. 50/k


K miles in 50 minutes
I.e. 1 mile in 50/k minutes
I.e. 10 miles in 10*50/k minutes = 500/k minutes

Answer : option A
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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 16 Feb 2017, 12:18
SajjadAhmad wrote:
If Jim drives k miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. 500/k
B. k/500
C. 60k
D. 10k
E. 50/k


Since rate = distance/time, Jim’s rate is k/50. We need to determine how many minutes it will take Jim to drive 10 miles.

time = distance/rate

time = 10/(k/50) = 10 x (50/k) = 500/k

Answer: A
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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 09 Oct 2018, 23:19
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Hi All,

We're told that Jim drives K miles in 50 MINUTES. We're asked how many MINUTES it will take him to drive 10 miles at the same rate. This question can be solved rather easily by TESTing VALUES.

Since K can be any positive value, we can set K = 10. Thus, we know that Jim drives 10 miles in 50 minutes. The question asks how minutes Jim drives 10 miles.... so the answer is 50. Thus, we're looking for an answer that equals 50 when K=10. Only one answer matches...

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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him  [#permalink]

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New post 10 Oct 2018, 05:54
1
SajjadAhmad wrote:
If Jim drives k miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. 500/k
B. k/500
C. 60k
D. 10k
E. 50/k

\(k\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{50}}\,\,{\text{minutes}}\,\,\,\,\,\,\,\)
\({\text{10}}\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{?}}\,\,{\text{minutes}}\)

This is a (direct) proportional problem, therefore a 10-year-child would probably do it (correctly) like that:

\(\frac{?}{{50}} = \frac{{10}}{k}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{500}}{k}\)

On the other hand, this is a trivial scenario for UNITS CONTROL, one of the most powerful tools of our method:

\(?\,\,\, = \,\,\,10\,\,{\text{miles}}\,\,\,\left( {\frac{{50\,\,{\text{minutes}}}}{{k\,\,{\text{miles}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{500}}{k}\,\,\,\,\left[ {{\text{minutes}}} \right]\)

Obs.: arrows indicate licit converter.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If Jim drives k miles in 50 minutes, how many minutes will it take him   [#permalink] 10 Oct 2018, 05:54
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