In an automobile race, the rate of one car was 120 mi/hr and the rate of another was 105 mi/hr. If the faster car finished the race 20 minutes before the slower one, what was the distance of the race?
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To find the distance of the race, we need to use the formula Distance = Speed × Time.
Let's assume the distance of the race is "d" miles.
The faster car traveled at a rate of 120 mi/hr, which means it covered the distance "d" in "t" hours. We can calculate "t" using the formula Time = Distance / Speed.
So, for the faster car: t = d / 120.
The slower car traveled at a rate of 105 mi/hr, which means it covered the distance "d" in (t + 20/60) hours. We add 20 minutes (converted to hours by dividing by 60) because the faster car finished 20 minutes before the slower one.
So, for the slower car: t + 20/60 = d / 105.
Now, we can set up an equation using the two expressions for "t" derived from the above formulas.
d / 120 = (d / 105) + 20/60.
Let's simplify this equation step by step:
Multiply both sides of the equation by 120 × 105 to eliminate the denominators:
105d = 120d + (20/60)(120 × 105).
Simplify further:
105d = 120d + 40.
120d - 105d = 40.
15d = 40.
Divide both sides of the equation by 15 to solve for "d":
d = 40 / 15.
d = 8/3 = 2.67 miles.
Therefore, the distance of the race is approximately 2.67 miles.