The danville Express travels 280 miles at a certain speed.If te speed were increased by 5 mph the trip could have been made in 1 hr less time.What was the actual speed?
To find the actual speed of the Danville Express, we can use the formula:
Speed = Distance / Time
Let's assume the actual speed of the Danville Express is "x" miles per hour.
According to the given information, the train traveled 280 miles. So, using the formula, we can calculate the original time taken to travel this distance:
Time = Distance / Speed
Time = 280 / x
Now, if the speed were increased by 5 mph, the new speed would be (x + 5) mph. The new time taken for the trip would be 1 hour less than the original time:
Time (after speed increase) = Time (original) - 1
Or,
280 / (x + 5) = 280 / x - 1
Now, we can solve this equation to find the value of x, which is the actual speed of the Danville Express.
To solve the equation:
280 / (x + 5) = 280 / x - 1
First, multiply both sides of the equation by x(x + 5) to eliminate fractions:
280x = 280(x + 5) - x(x + 5)
280x = 280x + 1400 - x^2 - 5x
Rearranging the equation:
0 = x^2 + 5x + 280x - 280x - 1400
Simplifying further:
0 = x^2 + 5x - 1400
Now, we need to factorize the quadratic equation to solve for the value of x:
0 = (x - 35)(x + 40)
Setting each factor to zero:
x - 35 = 0 or x + 40 = 0
Solving for x:
x = 35 or x = -40
Since negative speed does not make sense in this context, we can ignore the solution x = -40.
Therefore, the actual speed of the Danville Express is 35 miles per hour.