A car traveling at a certain constant speed takes 2 seconds

Question

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

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

Bunuel · Accepted Answer

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).

Answer: B.

KarishmaB · Answer

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

LalaB · Answer

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

MSoS · Answer

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

mvictor · Answer

a tricky one, that requires to read attentively what is asking
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.

SVaidyaraman · Answer

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

LakerFan24 · Answer

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.

Final answer: 72

JeffTargetTestPrep · Answer

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

Answer: B

mcelroytutoring · Answer

Attached is a visual that should help.

SVaidyaraman · Answer

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.

JeffTargetTestPrep · Answer

If a car is traveling at 75 km per hour, then the number of seconds (x) it takes to travel 1 km can be calculated using the following proportion (note that 1 hour = 3,600 seconds):

75/3600 = 1/x

75x = 3600

x = 48 sec.

Thus, it takes 48 seconds to travel 1 km if the speed is 75 km/h. Since the car actually takes 2 more seconds (i.e., 50 seconds) to travel 1 km, its speed (r) can be calculated using the following proportion:

r/3600 = 1/50

50r = 3600

r = 72 km/h

Answer: B

BrentGMATPrepNow · Answer

Let's start with a  word equation.

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

Answer: B

Sabby · Answer

Hi,

My rate is 75km/60min and my distance is 1km
time = distance/rate = 1/(75/60) = 60/75
60/75 = 12/15= 48/60 therefore it takes me 48 seconds and the time for the other speed rate will be 50
It takes me 50/60 sec to drive 1 km
rate = distance/ time = 1/(50/60) = 60/50 = 72/60

Answer B)

feeedi · Answer

Hi all, thank you for the details in the answer.

I have 2 questions :

1- The statement indiquest " At what speed, in kilometers per hour, is the car traveling? " doesn't that mean the average speed of the car for both distances?

2- Durring the Quant test we are not allowed to use the calculator, how can I make all this mental division in less than 2min and not make a mistakes. Is there any tips?

Many thanks

Dauan · Answer

I had a slightly different thought process from the above solutions.

Velocity = Distance / Time

Since the question is asked for a result in kmph, we should covert our numbers to km and hour units before calculation. Rather than dealing with multiple sec to hour conversions.

it would take 2*75 seconds longer to travel 75km, so:

Velocity = 75km / (1 hour + (2*75)/(3600) hours)) = 75km/(25/24)hours = 3*24kmph = 72 kmph

Archit3110 · Answer

we can write this as
1/75 + 2/3600 = 1/s
solve for s
1/75+1/1800 = 1/s
24+1/1800 = 1/s 
s = 1800/25 ; 72
option B

ThatDudeKnows · Answer

1km*\frac{1hr}{75kn}*\frac{3600sec}{1hr}

\frac{3600}{75}=\frac{4800}{100}=48

We need 50.

What can we plug in for the 75 in the first line above to make it so we end up with 50? Something where the numerator LOOKS like 50% of the denominator and the decimal places take care of themselves. Look at the answer choices; only one works with 36; 360; 3600; 0.36; 36,000,000; 0.00036 to give us something that's going to have an even 50. We need something that looks like 72; 72,000; 0.072; you get the point...we don't need to actually crunch the numbers at this stage.

Answer choice B.

*Note that rather than doing the division to calculate 3600/75, I recognized that I could multiply the denominator by 1.3333 to make it 100, so I did the same to the numerator. I think this is a useful little trick when they give you clumsy numbers.

pierjoejoe · Answer

i did the problem great, had all the equation set up, took me AGES to solve it due to my inability to perform basic arithmetic. are there any resources i can use to improve my skills in division/multiplication? i'd use also some apps or stuff like that.

TamirKalderon · Answer

First you need to check how many seconds does it take to travel 1 KM in 75KpH

So 75/60 is 5/4
5/4 Kilometer per minute

to make 5/4 KpM into 1Kpm (you need 1 Km) multiply by 4/5 minutes

So you get 1Km in 4/5 minute

4/5 minute is 48 seconds.

it takes 2 seconds  longer 
So it takes 48+2 seconds to travel 1km in the speed you're looking for

what is the speed in which you travel 1KM in 50 seconds?

50 seconds is 5/6 minute.
so you can travel 6/5 Km in a minute in that speed.

6/5 kilometer per minute * 60 minutes = 6*12 =  72

Ans: B

A car traveling at a certain constant speed takes 2 seconds

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