Problem Solving

AAPL wrote: ↑

Wed Apr 01, 2020 1:47 am

GMAT Paper Tests

A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take 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

OA B

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

Cheers,
Brent

AAPL wrote: ↑

Wed Apr 01, 2020 1:47 am

GMAT Paper Tests

A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take 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

OA B

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