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Intern  Joined: 19 Nov 2011
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A car traveling at a certain constant speed takes 2 seconds  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 61% (02:52) correct 39% (02:48) wrong based on 1297 sessions

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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

Originally posted by RadhaKrishnan on 28 Jan 2012, 04:10.
Last edited by Bunuel on 28 Jan 2012, 04:59, edited 1 time in total.
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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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GMAT 1: 690 Q47 V38 Re: A car traveling at a certain constant speed takes 2 seconds  [#permalink]

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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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1
1
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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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
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GMAT 1: 620 Q46 V30 Re: A car traveling at a certain constant speed takes 2 seconds  [#permalink]

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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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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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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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7
5
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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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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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.

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

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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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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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Attached is a visual that should help.
Attachments Screen Shot 2017-03-16 at 7.04.43 PM.png [ 136.03 KiB | Viewed 23433 times ]

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

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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

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

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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

1.Since we are given that it takes 2 seconds longer to travel 1 km in the current speed, we have to find the total number of seconds to travel 1 km in the hypothetical case
2.Speed of 75 km/hr is 0.8 min or 48 seconds to travel 1 km, the car currently takes 2 seconds longer i.e. 50 seconds to travel 1 km
3.We have to convert it to km/hr i.e., 1km/50 seconds = 1km /(50/3600)hr = 72 km/hr.
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A car traveling at a certain constant speed takes 2 seconds  [#permalink]

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t = d/r
r=d/t

t= 1/75 + 2/(60*60)

r = 1/1/75 + 2/(60*60)
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Re: A car traveling at a certain constant speed takes 2 seconds  [#permalink]

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Top Contributor
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

GIVEN: 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.
Let x = the car's speed

We can write: (travel time at x km per hour) = (travel time at 75 km per hour) + 2 seconds
Since the speeds are in km per HOUR, let's rewrite 2 seconds as 2/3600 hours (since there are 3600 second in one hour)

We get: (travel time at x km per hour) = (travel time at 75 km per hour) + 2/3600 hours
Or: (travel time at x km per hour) = (travel time at 75 km per hour) + 1/1800 hours

Travel time = distance/speed

We get: 1/x = 1/75 + 1/1800 hours
The least common multiple of the denominators is 1800x, so....
Multiply both sides by 1800x to get: 1800 = 24x + x
Simplify: 1800 = 25x
Solve: x = 1800/25 = 72

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

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$$rate * time = distance$$

rate and time are inversely proportional. So assuming the distance stays the same, doubling the time will half the rate. multiplying the time by 3/2 will result in a rate 2/3 as much.

75 * (1/75) = 1

The car goes 75 km per hour for 1/75 of an hour so for (3600/75)=48 seconds.

When the car takes two seconds longer it takes 50 seconds. The time increased by a factor of (25/24). The rate must therefore be multiplied by (24/25).

$$75(\frac{24}{25})=72$$
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Re: A car traveling at a certain constant speed takes 2 seconds  [#permalink]

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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

ffs.......

1/x - 1/75 = 2/3600
thats it Re: A car traveling at a certain constant speed takes 2 seconds   [#permalink] 15 Feb 2018, 06:39

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