Answer:
Step-by-step explanation:
distance = rate times time, so
distance
time = --------------
rate
Here the distance is 40 km and the rate is x. Then
40 km
time = -------------- = (40/x) hr
x km/hr
If the speed is reduced by 2 km/hr, we get:
40 km 40 km 40
time = ------------------------------- or time = ----------------------- = --------- hr
(x km/hr - 2 km/hr) (x - 2) (km/hr) x - 2
The difference between the times is:
40 40
-------- - --------- = 1 hr Solve this for the original speed, x
x - 2 x
40x - 40x + 80 80
----------------------- = 1 hr or ------------ = 1 or 80 = x^2 - 2x
x(x - 2) x(x - 2)
Rewriting this in standard quadratic form: x^2 - 2x - 80 = 0
Here a = 1, b = -2 and c = -80, and so the discriminant b^2 - 4ac is:
(-2)^2 - 4(1)(-80) = 324
The solutions are:
-(-2) ± √324 2 ± 18
x = -------------------- = ------------ = 1 ± 9, or 10 (discard the other root)
2 2
The original speed was 10 km/hr
