By increasing the speed of a car by 10km/hr the time of journey for a distance of 72 km is reduced by 36 min. Find the original speed of the car ?
Distance/rate = time
Let x = original speed in km per hour.
72/x - 72/(x+10) = 36/60
Solve for x.
To find the original speed of the car, we can use the formula for calculating speed:
Speed = Distance / Time
Let's say the original speed of the car is x km/hr.
The time taken to cover a distance of 72 km at the original speed would be:
Time = Distance / Speed = 72 / x
Now, let's consider the new speed of the car after increasing it by 10 km/hr. The new speed would be (x + 10) km/hr.
The time taken to cover the same distance of 72 km at the new speed would be:
Time = Distance / Speed = 72 / (x + 10)
According to the given information, the new time is 36 minutes (which is 36/60 = 0.6 hours) less than the original time, so:
72 / x - 72 / (x + 10) = 0.6
To solve this equation and find the value of x, we can use algebraic manipulations. Here's how:
1. Simplify the equation:
Multiply both sides of the equation by (x)(x + 10) to eliminate the denominators:
(x + 10)(72) - 72x = 0.6x(x)(x + 10)
2. Expand and simplify the equation:
72x + 720 - 72x = 0.6x^2 + 6x
Combine like terms:
720 = 0.6x^2 + 6x
3. Rearrange the equation to form a quadratic equation in standard form:
0.6x^2 + 6x - 720 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
For our equation, a = 0.6, b = 6, and c = -720.
Plugging these values into the quadratic formula, we get:
x = (-6 ± sqrt(6^2 - 4(0.6)(-720))) / (2(0.6))
Simplifying this further gives us:
x = (-6 ± sqrt(36 + 1728)) / 1.2
x = (-6 ± sqrt(1764)) / 1.2
x = (-6 ± 42) / 1.2
Taking both possibilities (positive and negative), we have two potential solutions:
1. x = (-6 + 42) / 1.2 = 36 / 1.2 = 30
2. x = (-6 - 42) / 1.2 = -48 / 1.2 = -40
Since the speed of a car cannot be negative, we can reject the solution x = -40.
Therefore, the original speed of the car is 30 km/hr.