speed takes 2 second longer to travel 1 kilometer

[Needgmat]

A car travelling at a certain constant speed takes 2 second longer to travel 1 kilometer that it would take to travel 1 kilometer at 75 kilometer per hours. At what speed in kilometers per hour, is the car traveling?

A) 71.5

B) 72

C) 72.5

D) 73

E) 73.5

OAB

Please explain.

Many thanks in advance.

Kavin

[GMATGuruNY]

A car travelling at a certain constant speed takes 2 second longer to travel 1 kilometer that it would take to travel 1 kilometer at 75 kilometer per hours. At what speed in kilometers per hour, is the car traveling?

A) 71.5

B) 72

C) 72.5

D) 73

E) 73.5

2 seconds longer per 1k = 150 seconds longer per 75k.
Since there are 3600 seconds in 1 hour, the additional time needed to travel 75k at the slower rate = 150/3600 = 1/24 hours.
Since the slower time is 1/24 longer than the faster time, the slower time is 25/24 of the faster time.
Time and rate are RECIPROCALS.
Since the slower time is 25/24 of the faster time, the slower rate is 24/25 of the faster rate:
(24/25)(75) = 72.

The correct answer is B.

[Needgmat]

2 seconds longer per 1k = 150 seconds longer per 75k.
Since there are 3600 seconds in 1 hour, the additional time needed to travel 75k at the slower rate = 150/3600 = 1/24 hours.
Since the slower time is 1/24 longer than the faster time, the slower time is 25/24 of the faster time.
Time and rate are RECIPROCALS.
Since the slower time is 25/24 of the faster time, the slower rate is 24/25 of the faster rate:
(24/25)(75) = 72.

The correct answer is B.

Hi GMATGuruNY ,

Thanks for your explanation.

Is there any other approach?

Many thanks in advance.

Kavin

[GMATGuruNY]

A car travelling at a certain constant speed takes 2 second longer to travel 1 kilometer that it would take to travel 1 kilometer at 75 kilometer per hours. At what speed in kilometers per hour, is the car traveling?

A) 71.5

B) 72

C) 72.5

D) 73

E) 73.5

Alternate approach:

(75 kilometers)/(1 hour) = (75 kilometers)/(3600 seconds) = (1 kilometer)/(3600/75 seconds) = (1 kilometer)/(48 seconds).

Since the car takes 2 seconds longer to travel 1 kilometer, the rate = (1 kilometer)/(50 seconds).

(1 kilometer)/(50 seconds) * (3600 seconds)/(1 hour) = 72 kilometers per hour.

The correct answer is B.

[NandishSS]

A car travelling at a certain constant speed takes 2 second longer to travel 1 kilometer that it would take to travel 1 kilometer at 75 kilometer per hours. At what speed in kilometers per hour, is the car traveling?

A) 71.5

B) 72

C) 72.5

D) 73

E) 73.5

OAB

Please explain.

Many thanks in advance.

Kavin

Alternate approach:

We know that Speed=Dist/Time

So Given T1-T2=2 sec

T1=1/S1, T2=1/75

(1/S1)-(1/75) = 2/3600 hr

On simplification S1=72Km/hr

OA:B

[Needgmat]

Alternate approach:

(75 kilometers)/(1 hour) = (75 kilometers)/(3600 seconds) = (1 kilometer)/(3600/75 seconds) = (1 kilometer)/(48 seconds).

Since the car takes 2 seconds longer to travel 1 kilometer, the rate = (1 kilometer)/(50 seconds).

(1 kilometer)/(50 seconds) * (3600 seconds)/(1 hour) = 72 kilometers per hour.

The correct answer is B.

Hi GMATGuruNY ,

Thank you so much for your explanation sir.

All clear.

Thanks,

Kavin