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# A car traveling at a certain constant speed takes 2 seconds

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A car traveling at a certain constant speed takes 2 seconds [#permalink]

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28 Jan 2012, 04:10
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A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Jan 2012, 04:59, edited 1 time in total.
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28 Jan 2012, 04:58
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A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

Many approaches are possible, one of them:

Let the distance be 1 kilometer.

Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;
Time to cover this distance at regular speed is 48+2=50 seconds = 50/3,600 hours = 1/72 hours;
So, we get that to cover 1 kilometer 1/72 hours is needed --> regular speed 72 kilometers per hour (rate is a reciprocal of time or rate=distance/time).

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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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30 Jan 2012, 01:11
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if 1 h=60*60 sec, then 2 sec =2/60*60=1/1800

1/1800+1/75=25/1800=1/72

since t=D/S and t=1/72 D=1 then S=72
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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30 Jan 2012, 03:41
B - 72

Original time in seconds: 60*60/75 = 48 --> Car need 48 seconds to travel 1 km
New car needs 2 more seconds to travel 1km --> 50 seconds to travel 1km

Speed (new car): 50 (seconds) / 3600 (1 hour in seconds) = 1 / 72 --> in 1 Minute the car travels 1 / 72. Thus 72km/h
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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27 Nov 2014, 14:50
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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27 Jan 2015, 03:24
Bunuel wrote:
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

Many approaches are possible, one of them:

Let the distance be 1 kilometer.

Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;
Time to cover this distance at regular speed is 48+2=50 seconds = 50/3,600 hours = 1/72 hours;
So, we get that to cover 1 kilometer 1/72 hours is needed --> regular speed 72 kilometers per hour (rate is a reciprocal of time or rate=distance/time).

Dear BUnuel,

Do you confirm this approach?

75 km is 75000 m and 1 hour is 60 min. so we have : 1000*60 /75000 = 4/5 min OR 4/5 *60 = 48 seconds
AS the promblem says take 2 seconds longer so we have 48+2 =50 seconds to cover 1 km or 1000 m
as we have formula like this: V*t = d so we have v*50= 1000 Or v= 1000/50 = 20 m/s

NOW convert to Km/h : 20 * 3600 (s) /1000 m = 72000/1000 = 72 km/h

Please confirm if this is true
Thanks
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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04 Feb 2015, 06:02
Bunuel wrote:
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

Many approaches are possible, one of them:

Let the distance be 1 kilometer.

Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;
Time to cover this distance at regular speed is 48+2=50 seconds = 50/3,600 hours = 1/72 hours;
So, we get that to cover 1 kilometer 1/72 hours is needed --> regular speed 72 kilometers per hour (rate is a reciprocal of time or rate=distance/time).

Dear BUnuel,

Do you confirm this approach?

75 km is 75000 m and 1 hour is 60 min. so we have : 1000*60 /75000 = 4/5 min OR 4/5 *60 = 48 seconds
AS the promblem says take 2 seconds longer so we have 48+2 =50 seconds to cover 1 km or 1000 m
as we have formula like this: V*t = d so we have v*50= 1000 Or v= 1000/50 = 20 m/s

NOW convert to Km/h : 20 * 3600 (s) /1000 m = 72000/1000 = 72 km/h

Please confirm if this is true
Thanks

I'm not Bunuel but I don't see anything wrong in the approach.
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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31 Oct 2015, 12:42
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so the car travels 75km/hr. to cover 1 km, it would travel at 1/75 hours or 1/75 * 60 * 60 seconds. Simplify 75 and one of 60 by 15, and get 1/5 * 4 * 60 -> simplify again 5 and 60 and get 1*4*12 = 48 seconds. We know that the car makes 1 km in 48 seconds.

we know that the car spends 2 seconds more, and this is 48+2 seconds, or 50 seconds. We have the distance, and we have the time. We can solve for rate:
R = Distance/Time = 1km/50sec, for the sake of getting rid of 50 sec in the denominator, divide 1km by 50 and get 0.02km/second
now, 1 hour has 3600 seconds. Multiply 3,600 sec by 0.02km or 36*2 = 72km/h.
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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31 Oct 2015, 20:14
faster car travels 1 kilometer in 1/75 hour
slower car travels 1 kilometer in 1/75+1/1800 hour
1/75+1/1800=25/1800=1/72 hour
inverting time and rate, slower car travels at 72 kph
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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01 Nov 2015, 22:13
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A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

If I had only 10 seconds to read the question and mark, I would mark it as (B) 72. The reason is the kind of numbers we are dealing with. 1 hour has 3600 seconds (which is a multiple of 2, 3 and 5, 18 etc). 75 km is again a multiple of 3 and 5. Getting 71 or 73 out of these numbers wouldn't really work out. It will be unusual to get decimals. So my best blind guess would be 72.

If I did have some time, I would use the unitary method on it:

Case 1:
75 kms in 3600 secs
1 km in 3600/75 = 48 secs

Case 2:
In (48+2) = 50 secs, it covers 1 km
In 3600 secs, it will cover (1/50) * 3600 = 72 km

Speed = 72 km/hr
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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02 Nov 2015, 01:13
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

Variables given :

d1= 1 km

d2=1 km
s2=75

Variables expressed in terms of another:-

t1 = t2+ 2/3600

To find :

s1=?

We need to form two equations based on the above:

We know distance travelled is the same. So equate distances.

s1*t1=s2*t2
s1*(t2+2/3600)=75*t2 --- (1)

We also know the values of d2 and s2. So we can find t2.
d2=s2*t2
i.e., 1=75*t2 => t2=1/75 hr

Substituting the value of t2 in (1), we get s1=72 km/hr
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A car traveling at a certain constant speed takes 2 seconds [#permalink]

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07 Dec 2015, 08:17
Problems similar to this one?
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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04 Jul 2016, 08:22
lolivaresfer wrote:
Problems similar to this one?

conversion-problems-175012.html
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A car traveling at a certain constant speed takes 2 seconds [#permalink]

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22 Feb 2017, 20:07
This is a rarity, but I like GMATPrep's solution to this problem. I'll do my best to rephrase (btw yes, this is a conversion problem):

First, I like to set up the initial conversion (for the car in the 1st scenario):

(75 km/1hr)*(1hr/60min)*(1min/60sec) --> 75 km/3600 sec. You can simplify this further into: 1 km/48 sec.

Now, let's take the same car in a different scenario (2nd):

1 km/48+2 seconds --> 1 km/50 seconds. NOTE: the Q asks for speed in KM per HOUR. So we need to convert from seconds into hours. 50 seconds goes into 3600 seconds 72x.

kudos always appreciated if this helps
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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09 Mar 2017, 21:57
With the current speed, the drive takes 2 seconds more to travel every km and 2*75 = 150 more seconds to travel 75 km. So it takes him 1+1/24=25/24 hours to travel 75 km
It means in 1 hour, he can travel 75*24/25=72 km =>> his speed = 72km/h =>> Answer B
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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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15 Mar 2017, 16:38
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

We can let r = the speed of the car in km per hour; thus it would take the car 1/r hour to travel 1 km. If the car traveled at 75 km per hour, then it would take the car 1/75 hour to travel 1 km.

We are given that the car would be 2 seconds faster traveling 1 km had it traveled at 75 km per hour. Since 2 sec = 1/1800 hour, we can create the following equation:

1/75 + 1/1800 = 1/r

Multiplying the entire equation by 1800r, we have:

24r + r = 1800

25r = 1800

r = 72

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Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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16 Mar 2017, 19:05
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Attached is a visual that should help.
Attachments

Screen Shot 2017-03-16 at 7.04.43 PM.png [ 136.03 KiB | Viewed 1082 times ]

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A car traveling at a certain constant speed takes 2 seconds [#permalink]

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16 Mar 2017, 21:38
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

75 kph=4/5 minute, or 48 seconds, per k
48+2=50 seconds=5/6 minute
60/(5/6)=72 kph
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A car traveling at a certain constant speed takes 2 seconds [#permalink]

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17 Mar 2017, 01:24
Let the speed be v
1/v =2/3600 + 1/75
solving v we get v = 72.
A car traveling at a certain constant speed takes 2 seconds   [#permalink] 17 Mar 2017, 01:24
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