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While driving from A-ville to B-town, Harriet drove at a constant spee

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While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

A. 138
B. 148
C. 150
D. 162
E. 168

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 19 Feb 2015, 10:00
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X = Time from A to B
Y = Time from B to A
X+Y=5 hrs total travel time
115X=135Y since the distances are the same

X+Y=5 => 135X+135Y=675
115X=135Y => 115X-135Y=0
Combined you get
250X=675 hrs
X=2.7 hrs * 60 mins/hr= 162

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 19 Feb 2015, 10:27
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Its D.
Here it goes:
Distance will be same both sides... hence total distance will D+D= 2D
Total time given+ 5hrs
Speed per side also given.. 115km/ph and 135 km/ph
Speed= Distanct/Time
D/s1 + D/s2= total time
(d/115) + (d/135) = 5
solving it D comes to 621 km
Hence each side is D/2 : 621/2 = 310.5 km
Time for first journey is 310.5/115 which is 162 mins
Thanks

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 19 Feb 2015, 11:49
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Celestial09 wrote:
Its D.
Here it goes:
Distance will be same both sides... hence total distance will D+D= 2D
Total time given+ 5hrs
Speed per side also given.. 115km/ph and 135 km/ph
Speed= Distanct/Time
D/s1 + D/s2= total time
(d/115) + (d/135) = 5
solving it D comes to 621 km
Hence each side is D/2 : 621/2 = 310.5 km
Time for first journey is 310.5/115 which is 162 mins
Thanks

Kudos please if my solution is correct!



Hello,

I have struggles coming from (D/115) + (D/135) = 5
to D = 621

could you explain the calculation steps ?

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 19 Feb 2015, 12:06
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Hello!
Thanks for addressing your doubt. here it goes:
(d/115) + (d/135) = 5 kindly note.. its addition of two fractions... so I kindly take 5 common from both denominators... hence you will be left with d/23 + d/27 and that 5 will cross multiply to other side of equation.. resulting
d/23 + d/27 = 25
then kindly solve it ... 27d +23 d = 25*23*27
d will come down to 310.5
which i particularly took as total distance 310.5*2 = 621 km
hope it makes sense.
thanks

LaxAvenger wrote:
Celestial09 wrote:
Its D.
Here it goes:
Distance will be same both sides... hence total distance will D+D= 2D
Total time given+ 5hrs
Speed per side also given.. 115km/ph and 135 km/ph
Speed= Distanct/Time
D/s1 + D/s2= total time
(d/115) + (d/135) = 5
solving it D comes to 621 km
Hence each side is D/2 : 621/2 = 310.5 km
Time for first journey is 310.5/115 which is 162 mins
Thanks

Kudos please if my solution is correct!



Hello,

I have struggles coming from (D/115) + (D/135) = 5
to D = 621

could you explain the calculation steps ?

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 22 Feb 2015, 11:37
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Bunuel wrote:
While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

A. 138
B. 148
C. 150
D. 162
E. 168

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION
Attachment:
harriettakestrip_text.PNG
harriettakestrip_text.PNG [ 25.95 KiB | Viewed 4449 times ]

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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Answer = D = 162

Let distance between A & B = d

Setting up the time equation

\(\frac{d}{115} + \frac{d}{135}= 5\)

\(d = \frac{23 * 27}{2}\) (Need not have to solve)

Time required in minutes from A to B \(= \frac{23*27}{2*115} * 60 = 162\)
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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 23 Mar 2015, 07:48
Distance from A to B is the same as distance from B to A. Hence

115x=135y
x/y=135/115 => x/y=27/23
so x= 27/50 of the total time (50=27+23).
total time x+y=5h= 300minutes,

x= 300m*(27/50)= 162m

Answer. D

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 19 Jul 2015, 10:00
Hi everyone,

I don't see why we divide the distance 625 by 250 and not 115, while Harriet drives from A to B at 115mph...
Does not make sense to me.

But at the same time, dividing 625 by 115 gives us a time of 5+ hours, which is also impossible because the whole trip A --> B --> A takes 5 hours.
Can someone please give some insights?

Many thanks in advance

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While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 04 Sep 2016, 12:17
5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.

Now let plug in ans. D or E and verify which one give same distance on each leg.

D. t= 162min
* leg A-B ---> d = 115.162/60 = 18630/60
* leg B-A ----> d = 135*138/60 = 18630/60

so the correct ans. is D

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 13 Nov 2016, 09:35
Rates and Distance: Q: Find t on the way in?
When you are given the same distance on the way in and back. ex: d
and you are given the rates for back and forth. ex: 115 and 135
and you are given the total time. ex: 5

step1: organize the formulas like below. Use 5-t for the time on the way back = very important.

rt=d
115 (t) = d
135 (5-t) = d

step2: Make the two equations equal and solve for t

115(t) = 135 (5-t)
t= 27/10 hours

step3: check the convention of time that the question wants you to answer and convert if needed

In this question, you are asked for minutes, so you need to do one more thing before jumping into the answers

27/10 hours * 60minutes = 162 minutes

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 13 Nov 2016, 09:49
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Distance taken = speed*time
Let Harriet took x hrs to go from A to B and y hrs to come from B to A.
Distance=115*x=135*y
x+y=5 (total time=5 hrs.)
we need to find x.
y=5-x
Substituting in Distance equation.
115*x=135(5-x)
Solve to get x=2.7hrs
2.7*60=162mins.
Answer=D.


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While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 13 Nov 2016, 11:54
Bunuel wrote:
While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

A. 138
B. 148
C. 150
D. 162
E. 168

Kudos for a correct solution.


average speed for round trip≈125 kph
125*5=625 round trip miles
625/2=312.5 one way miles
312.5/115=2.72 hours
2.72*60=163.2 minutes
closest to 162
D

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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New post 22 Nov 2016, 01:53
Bunuel wrote:
While driving from A-ville to B-town, Harriet drove at a constant speed of 115 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 135 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

A. 138
B. 148
C. 150
D. 162
E. 168

Kudos for a correct solution.


distance travelled is the same in each direction thus time is inversely proportional to speed , total time = 5 , let first leg time t and 2nd leg time = 5-t

115/135 = 5-t / t thus , t in hours = 5*27/50 , in minutes = 300*27/50 = 6*27 = 162..........D

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee [#permalink]

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Re: While driving from A-ville to B-town, Harriet drove at a constant spee   [#permalink] 03 Dec 2017, 12:54
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