The travel time between two cities is inversely proportional to the average speed. A train travels between the cities in 3 hours at an average speed of 65mph. How lone would it take to travel between the cities at an average speed of 80 mph?
How lone would it take to travel between the cities at an average some of 80mph?
How long***
65 * 3 = 195 miles
195 / 80 = 2.44 hours
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To solve this problem, we need to use the concept of inverse proportionality and create an equation that relates the travel time and the average speed.
Let's denote the travel time as "t" and the average speed as "s". According to the problem, the travel time and average speed are inversely proportional, which means that as the average speed increases, the travel time decreases by the same factor.
We can write this relationship as:
t ∝ 1/s
To find the specific equation relating t and s, we need to introduce a constant of proportionality. Let's call it "k". Therefore, we can rewrite the equation as:
t = k/s
Now, we can use the given information to find the value of "k". The problem states that the train travels between the cities in 3 hours at an average speed of 65 mph. Substituting these values into the equation, we have:
3 = k/65
Now we can solve for k:
k = 3 * 65
k = 195
Now we have the value of the constant of proportionality. We can substitute it back into our equation:
t = 195/s
Finally, we can use the equation to calculate the travel time when the average speed is 80 mph. By substituting s = 80:
t = 195/80
Calculating this expression, we find:
t ≈ 2.4375 hours (approximately 2 hours and 26 minutes)
Therefore, it would take approximately 2 hours and 26 minutes to travel between the cities at an average speed of 80 mph.