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A transportation company is interested in knowing the amount of time it takes for the different type of vehicles
they own to travel certain distances based on their different speeds.
A car travels 180 miles in the same time that a truck travels 120 miles.
If the car’s speed is 20 miles per hour faster than the truck’s,
find the car’s speed and the truck’s speed. Make sure to show all your work.
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Let x be the car's speed, in miles per hour.
Then the speed of the truck is (x-20) miles per hour.
The time for the car to travel 180 km is hours.
The time for the truck to travel the same distance id hours.
This time is the same
= .
Simplify and find x
180*(x-20) = 120*x,
3*(x-20) = 2*x
3x - 60 = 2x
3x - 2x = 60
x = 60.
Thus the speed of the car is 60 mph; the speed of the truck is 60-20 = 40 mph.
CHECK. The time for the car to travel 180 miles is = 3 hours.
The time for the truck to travel 120 miles is = 3 hours.
The time is the same - so the answer is correct.
Solved.
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I would like to notice that in this problem the first phrase/sentence
can be (and should be) omitted without compromising the meaning of the problem.
In other words, this phrase is absolutely unnecessary and totally excessive.
Professional Math writers never include unnecessary and/or excessive phrases into their Math compositions.
Good style of Math writing does not allow it.
It is what makes a distinction between professional and unprofessional Math writers.