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Every day John walks at a constant speed, V1, for 30 minutes

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Every day John walks at a constant speed, V1, for 30 minutes  [#permalink]

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New post 30 Jul 2019, 20:43
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (03:16) correct 43% (03:16) wrong based on 37 sessions

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Every day John walks at a constant speed, V1, for 30 minutes. On a particular day, after walking for 10 minutes at V1, he rested for 5 minutes. He finished the remaining distance of his regular walk at a constant speed, V2, in another 30 minutes. On that day, find the ratio of V2 and his average speed (average speed is total distance covered divided by total time taken including resting time).

A. 1:1
B. 1:2
C. 2:3
D. 2:1
E. 3:2

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Re: Every day John walks at a constant speed, V1, for 30 minutes  [#permalink]

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New post 30 Jul 2019, 21:14
1
Every day John walks at a constant speed, V1, for 30 minutes.
total distance = 30V1

one day walking at V1 for 10 minutes --distance covered = 10V1
after walking take a rest of 5 minutes

then walking the remaining distance = 30V1-10V1 =20V1
he covered the remaining distance at V2 in 30 minutes = 30V2 (distance covered during this time)

20V1 = 30 V2
V2 = \(\frac{2V1}{3}\)

average speed = \(\frac{total distance}{total time}\)
average speed = \(\frac{30V1}{45}\) (Total time = time taken with V1+ time taken with V2 + rest time)
=\(\frac{2V1}{3}\)

RATIO of V2 and his average speed = \(\frac{V2}{2V1/3}\)
= V2*\(\frac{3}{2V1}\)
=\(\frac{2V1}{3}\)*\(\frac{3}{2V1}\)=1

SO ratio is 1:1
A is the answer
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Re: Every day John walks at a constant speed, V1, for 30 minutes  [#permalink]

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New post 03 Aug 2019, 23:32
Let the distance of his regular walk be D which he usually covers in 30 mins at a speed of V1.

On the day in question, he covers (1/3)rd of D in 10 minutes which leaves (2/3)*D which he covers in 30 mins at a speed of V2.
V2=(2/3)*D/30
He covers the entire distance D in 45 mins (10+5+30). Thus, his average speed (VA) = D/45.

V2/VA = {(2/3)*D/30}/(D/45) = (2/90)*45 = 1. ANS: 1:1 (A)
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Re: Every day John walks at a constant speed, V1, for 30 minutes   [#permalink] 03 Aug 2019, 23:32
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