A car travel at constant speed from Q to R, a distance of 300 km apart. If the drive increases the speed by 5 km/h, the journey will take 2 hours less. Find the original speed of the car.
Original speed --- x km/h
time at original speed = 300/x hrs
new speed ---- x+5
time at new speed = 300/(x+5)
300/x - 300/(x+5) = 2
solve for x, after multiplying all terms by x(x+5) to get your quadratic
To solve this problem, let's denote the original speed of the car as "x" km/h.
Given that the distance between points Q and R is 300 km and the car travels at a constant speed, we can use the formula Speed = Distance / Time to set up the following equation:
x = 300 / t1
where t1 represents the original time taken to travel from point Q to R at the speed of x km/h.
Now, if the driver increases the speed by 5 km/h, the new speed becomes x + 5 km/h. The distance remains the same (300 km). Since the journey now takes 2 hours less than the original time, we can set up another equation using the same formula:
x + 5 = 300 / (t1 - 2)
where (t1 - 2) represents the new time taken to travel from point Q to R.
Now, we have two equations:
x = 300 / t1
x + 5 = 300 / (t1 - 2)
To solve for x (the original speed of the car), we can use the method of substitution. Rearrange the first equation to t1 = 300 / x and substitute it into the second equation:
x + 5 = 300 / ((300 / x) - 2)
To simplify further, we can multiply both sides of the equation by ((300 / x) - 2) to eliminate the denominator:
x((300 / x) - 2) + 5((300 / x) - 2) = 300
Simplifying the equation further:
300 - 2x + 1500 / x - 10 = 300
Multiply through by x to eliminate the fractions:
300x - 2x^2 + 1500 - 10x = 300x
Rearrange the equation:
-2x^2 + 1500 - 10x = 0
Divide through by -2:
x^2 + 5x - 750 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula.
By factoring or using the quadratic formula, we find that the solutions are x = 25 and x = -30. Since we are looking for the original speed of the car, we can conclude that the original speed of the car is 25 km/h.
Therefore, the original speed of the car is 25 km/h.