hi can you help me with this problem please, thank you.-----------------
If the speed of an experimental car is decreased by 8km/h it completes a 140 km trip in 2 hours more than had it been traveling at its usual speed. Determine its usual speed.
Let S=usual speed,
Then S-8=experimental speed.
Taking the difference between the "experimental time" and "usual time", we get:
140/S - 140/(S-8) = 2
Solve for S.
The equation should read:
140/(S-8) - 140/S = 2
Of course, I can help you with that problem!
To solve this problem, we need to set up an equation based on the given information and then solve for the unknown variable, which is the usual speed of the car. Here's how we can approach it step by step:
1. Let's assume the usual speed of the car is "x" km/h.
2. According to the problem, if the speed of the car is decreased by 8 km/h, it takes 2 hours longer to complete the 140 km trip.
3. So, if the car is traveling at a speed of (x - 8) km/h, it takes 2 hours more.
4. We can use the formula: time = distance / speed to set up an equation. The time taken at the usual speed (x km/h) is 140 km divided by x km/h, and the time taken when the speed is decreased by 8 km/h is 140 km divided by (x - 8) km/h plus 2 hours.
Putting it all together, we have:
140 / x = 140 / (x - 8) + 2
To solve the equation, we can start by multiplying both sides of the equation by x times (x - 8) to eliminate the denominators:
140(x - 8) = 140x + 2x(x - 8)
Now we simplify and solve for x:
140x - 1120 = 140x + 2x² - 16x
0 = 2x² - 16x + 1120
Solving this quadratic equation yields two possible answers for x, the usual speed of the car. We can either factor the quadratic or use the quadratic formula.
Factoring the equation may not work in this case since the coefficients do not have a common factor. So, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation 2x² - 16x + 1120 = 0, the values of a, b, and c are:
a = 2
b = -16
c = 1120
Now, substituting these values into the quadratic formula:
x = (-(-16) ± √((-16)² - 4 * 2 * 1120)) / (2 * 2)
x = (16 ± √(256 - 8960)) / 4
x = (16 ± √(-8704)) / 4
Since we have a negative value under the square root, it means there are no real solutions for the usual speed of the car. This result suggests there might be an error in the problem or the given information.
So, unfortunately, without further clarification or correction of the problem, we cannot determine the usual speed of the car.