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A car traveling at a certain constant speed takes 2 seconds
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24 Jun 2020, 09:25
24 Jun 2020, 09:25
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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
A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5
Re: A car traveling at a certain constant speed takes 2 seconds
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24 Jun 2020, 09:26
24 Jun 2020, 09:26
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A car traveling at a certain constant speed takes 2 seconds
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24 Jun 2020, 09:35
24 Jun 2020, 09:35
1
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
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
