When the speed is increased by 4 miles per hour, it takes 4 hour less to cover a distance of 32 km. Find the previous speed.
Let's denote the original speed as "x" miles per hour.
When the speed is increased by 4 miles per hour, the new speed becomes "x + 4" miles per hour.
We are given that when the speed is increased by 4 miles per hour, it takes 4 hours less to cover a distance of 32 km. We can set up the equation using the formula:
Time = Distance / Speed
Original time = 32 km / x New time = 32 km / (x + 4)
According to the given information, the new time is 4 hours less than the original time. So, we can write:
Original time - New time = 4 hours
32 km / x - 32 km / (x + 4) = 4
To solve this equation, let's first find a common denominator, which is x(x + 4):
(32(x + 4) - 32x) / (x(x + 4)) = 4
Now, simplify the equation:
(32x + 128 - 32x) / (x(x + 4)) = 4
128 / (x(x + 4)) = 4
Now, cross-multiply:
128 = 4(x(x + 4))
Divide both sides by 4:
32 = x(x + 4)
Now, let's solve for x by factoring:
x(x + 4) = 32
x² + 4x - 32 = 0
Now, we can factor the quadratic equation:
(x + 8)(x - 4) = 0
Setting each factor equal to zero:
x + 8 = 0 or x - 4 = 0
If x + 8 = 0, then x = -8, but since we're looking for a speed, it must be positive.
If x - 4 = 0, then x = 4.
So, the previous speed (original speed) was 4 km per hour.
Related Question
View MorePromotion
Download Our Mobile Apps
