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A cyclist is travelling on a square path having curved corners as show

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Bunuel
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A cyclist is travelling on a square path having curved corners as show [#permalink] New post   29 Jan 2021, 07:45
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42% (03:15) correct 58% (02:30) wrong based on 24 sessions
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A cyclist is travelling on a square path having curved corners as shown in the figure. Each curved corner is a quarter circle of radius 42 m. If he travels on the curved path at a speed that is 2/3 rd of his speed on the straight path and traces the complete path once in 15 minutes, what is his speed on the straight path?

(A) 2.20 km/hr
(B) 6.65 km/hr
(C) 8.24 km/h
(D) 10 km/h
(E) 12.48 km/hr

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meanup
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Re: A cyclist is travelling on a square path having curved corners as show [#permalink] New post   29 Jan 2021, 09:42
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Bunuel wrote:

A cyclist is travelling on a square path having curved corners as shown in the figure. Each curved corner is a quarter circle of radius 42 m. If he travels on the curved path at a speed that is 32rd of his speed on the straight path and traces the complete path once in 15 minutes, what is his speed on the straight path?

(A) 2.20 km/hr
(B) 6.65 km/hr
(C) 8.24 km/h
(D) 10 km/h
(E) 12.48 km/hr

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Attachment:
2021-01-28_22-01-22.png


Dear Bunuel, please review this question. I believe it should be \(\frac{2}{3}\)
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Re: A cyclist is travelling on a square path having curved corners as show [#permalink] New post   29 Jan 2021, 09:45
Let the speed be \(x\) \(\frac{m}{s}\).

Distance covered on the straight path \(= 4*(500-84)=(4*416)\) m

Distance covered in curved path \(=2πr= 2* \frac{22}{7} *42 = 12 *22\) m

Therefore,

\(\frac{4*416}{x} + 12*22*\frac{3}{2x}=15*60\)

\(\frac{1}{x}*(1664+396)=15*60\)

\(x=\frac{2060}{15*60}=\frac{206}{9}*\frac{18}{5}=8.24\) km/hr

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Re: A cyclist is travelling on a square path having curved corners as show [#permalink] New post   29 Jan 2021, 10:16
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meanup wrote:
Bunuel wrote:

A cyclist is travelling on a square path having curved corners as shown in the figure. Each curved corner is a quarter circle of radius 42 m. If he travels on the curved path at a speed that is 32rd of his speed on the straight path and traces the complete path once in 15 minutes, what is his speed on the straight path?

(A) 2.20 km/hr
(B) 6.65 km/hr
(C) 8.24 km/h
(D) 10 km/h
(E) 12.48 km/hr

Show Spoiler
Attachment:
2021-01-28_22-01-22.png


Dear Bunuel, please review this question. I believe it should be \(\frac{2}{3}\)

______________
Fixed. Thank you!
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gmatclubot
Re: A cyclist is travelling on a square path having curved corners as show [#permalink]
29 Jan 2021, 10:16
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