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# Peter traveled from home to school and returned along the same route

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
Peter traveled from home to school and returned along the same route  [#permalink]

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04 Nov 2019, 02:33
00:00

Difficulty:

95% (hard)

Question Stats:

33% (02:23) correct 67% (01:56) wrong based on 49 sessions

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Peter traveled from home to school and returned along the same route in the evening at a speed of 6 mph. What was Peter's average speed for the two way trip

(1) Peter's average speed is 0.8 mph greater than his speed from home to school

(2) Peter traveled from home to school at 4mph

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Peter traveled from home to school and returned along the same route  [#permalink]

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Updated on: 07 Nov 2019, 08:26
Bunuel wrote:
Peter traveled from home to school and returned along the same route in the evening at a speed of 6 mph. What was Peter's average speed for the two way trip

(1) Peter's average speed is 0.8 mph greater than his speed from home to school

(2) Peter traveled from home to school at 4mph

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need to find
2ab/a+b
b=6
#1
Peter's average speed is 0.8 mph greater than his speed from home to school
12a/(a+6)= .8+a
solving for a we get a quadratic and two values
insufficient
#2
Peter traveled from home to school at 4mph
so b= 2
2*4*2/6 = sufficient
IMO B

Originally posted by Archit3110 on 04 Nov 2019, 02:44.
Last edited by Archit3110 on 07 Nov 2019, 08:26, edited 2 times in total.
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Peter traveled from home to school and returned along the same route  [#permalink]

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04 Nov 2019, 02:50
Peter traveled from home to school and returned along the same route in the evening at a speed of 6 mph. What was Peter's average speed for the two way trip

S1=D/T1; S2=D/T2; S2=6

average speed= total distance/total time= 2D/T1+T2

T1=D/S1, T2=D/S2

average speed= 2*S1*S2/S1+S2; S2=6----EQN1

therefore we need the value of S1 to solve the question!

(1) Peter's average speed is 0.8 mph greater than his speed from home to school

average speed= 0.8+S1
S1= average speed-0.8
substitute in EQN 1

(0.8+S1)(6+S1)=12*S1
S1^2+5.2S1+4=0

determinant is positive therefore we have two values for S1----> two values for average speed --- insufficient!

(2) Peter traveled from home to school at 4mph
S1= 4 sufficient!!

remember in data sufficiency we do not need to arrive at the answer we just need to see if the options are sufficient!
B is the correct answer!!
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Peter traveled from home to school and returned along the same route   [#permalink] 04 Nov 2019, 02:50
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# Peter traveled from home to school and returned along the same route

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