Carcass 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
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