The Danville Epress travels 280mi at a certain speed.If the speed had been increased by 5mph the trip could have been made in 1 hour less time.Find the actual speed.
To find the actual speed of the Danville Express, we can solve this problem using algebra. Let's assume the actual speed of the Danville Express is x mph.
According to the problem statement, the Danville Express travels 280 miles at a certain speed (x mph). If the speed had been increased by 5 mph, the trip could have been made in 1 hour less time.
Let's set up the equation based on the given information:
Original time = Distance / Speed
New time = Distance / (Speed + 5)
We know that the original time minus 1 hour equals the new time:
Original time - 1 = New time
Let's substitute the formulas for the times into the equation:
280 / x - 1 = 280 / (x + 5)
To solve this equation, we can find a common denominator:
280(x + 5) / x(x + 5) - x(x + 5) / x(x + 5) = 280(x + 5) / (x + 5)
Now, let's simplify the equation:
280(x + 5) - x(x + 5) = 280
280x + 1400 - x^2 - 5x = 280
Rearrange the equation:
x^2 + 5x - 280x - 1400 + 280 = 0
Combine the like terms:
x^2 - 275x - 1120 = 0
Now, let's factor this quadratic equation:
(x - 40)(x + 35) = 0
Setting each factor equal to zero:
x - 40 = 0 or x + 35 = 0
Solving for x:
x = 40 or x = -35
Since speed cannot be negative, we ignore the solution x = -35.
Therefore, the actual speed of the Danville Express is 40 mph.