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Noelle's walk

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by hansoo » Tue Sep 08, 2009 8:05 am
Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour?

a) 6.75
b) 7.00
c) 7.25
d) 7.50
e) 7.75
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by Nermal » Tue Sep 08, 2009 8:47 am
IMO D (7.5)
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by bharathh » Tue Sep 08, 2009 8:59 am
D IMO as well

Speed from A -> B is 5kmph.

Since the average I want is 6kmph... I'll choose a number divisible by 5 and 6... Let's take the distance as 30km

Time taken for A->B at 5kmph = 30/5 = 6 hrs

Total distance if I want to travel to B and back = 30+30 = 60km

Average speed = 6kmph. So total time spent travelling = 60/6 = 10 hrs

I've already spent 6 hrs getting to B .. So I have to spend 4 hrs travelling back.

Speed reqd is 30/4 = 7.5
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by hansoo » Thu Sep 10, 2009 1:59 pm
Great responses guys! The official answer is D.

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by vivek.kapoor83 » Fri Sep 11, 2009 9:39 am
let distance between A n B = 10kms
avg speed= total distance/total time

6= 20/2+x
12+6x= 20
x= 8/6=4/3

so from B to A person takes = 4 hr
s=d/t
s=10/(4/3)=30/4=7.5km/hr shld bd speed
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by Scott@TargetTestPrep » Fri Dec 15, 2017 7:03 am
hansoo wrote:Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 6 kilometers per hour?

a) 6.75
b) 7.00
c) 7.25
d) 7.50
e) 7.75
We can let the distance from point A to point B = d, so the entire trip is 2d.

Thus, the time to go from point A to point B is d/5. If we let r = Noelle's walking rate from point B to point A, then her time is d/r. We can plug all of our values into the average rate formula:

average rate = (distance 1 + distance 2)/(time 1 + time 2)

6 = 2d/(d/5 + d/r)

6(d/5 + d/r) = 2d

6d/5 + 6d/r = 2d

6/5 + 6/r = 2

6/r = 4/5

30 = 4r

7.5 = r

Answer: D

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