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Tom travels the same distance in 4 steps as Alice travels in 5 steps.

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Math Revolution GMAT Instructor
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GMAT 1: 760 Q51 V42
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Tom travels the same distance in 4 steps as Alice travels in 5 steps.  [#permalink]

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New post 17 Jul 2019, 01:35
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[GMAT math practice question]

Tom travels the same distance in \(4\) steps as Alice travels in \(5\) steps. If the length of one of Alice’s steps is \(36 cm\), what distance, in \(cm\), does Tom cover in \(18\) steps?

\(A. 5184\)

\(B. 3688\)

\(C. 1800\)

\(D. 1243\)

\(E. 810\)

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Re: Tom travels the same distance in 4 steps as Alice travels in 5 steps.  [#permalink]

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New post 17 Jul 2019, 01:38
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MathRevolution wrote:
[GMAT math practice question]

Tom travels the same distance in \(4\) steps as Alice travels in \(5\) steps. If the length of one of Alice’s steps is \(36 cm\), what distance, in \(cm\), does Tom cover in \(18\) steps?

\(A. 5184\)

\(B. 3688\)

\(C. 1800\)

\(D. 1243\)

\(E. 810\)


Let length of TOM's step be t cm
4t = 5*36 = 180 cm
t=45 cm
18t = 45*18 = 810 cm

IMO E
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Re: Tom travels the same distance in 4 steps as Alice travels in 5 steps.  [#permalink]

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New post 17 Jul 2019, 04:15
MathRevolution wrote:
[GMAT math practice question]

Tom travels the same distance in \(4\) steps as Alice travels in \(5\) steps. If the length of one of Alice’s steps is \(36 cm\), what distance, in \(cm\), does Tom cover in \(18\) steps?

\(A. 5184\)

\(B. 3688\)

\(C. 1800\)

\(D. 1243\)

\(E. 810\)


Since each of Alice's steps = 36 cm, the distance traveled by Alice in 5 steps = 5*36 = 180 cm.
Since Tom requires only 4 steps to travel this 180-cm distance, each of Tom's steps = 180/4 = 45 cm.
Thus, the distance traveled by Tom in 18 steps = 18*45 = 810 cm.

.
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Re: Tom travels the same distance in 4 steps as Alice travels in 5 steps.  [#permalink]

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New post 19 Jul 2019, 01:05
=>

Let \(t\) and \(a\) be stride-lengths of Tom and Alice, respectively.
Then \(4t = 5a\) and \(a = 36.\)

So, \(t = (\frac{5}{4})a = (\frac{5}{4})*36 = 45 cm.\)

It follows that \(18t = 18*45 = 810 cm.\)

Therefore, E is the answer.
Answer: E
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Re: Tom travels the same distance in 4 steps as Alice travels in 5 steps.   [#permalink] 19 Jul 2019, 01:05
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