An automobile travels 280km at a certain speed. if the speed had been 5 km/h faster, the trip would have been made in 1 hour less time. find the original speed of the automobile.

If it they travel at the same speed then acceleration will be 0

Using the equation s= ut + 1/2 a t ^2
Since a is 0
S= ut

From this we can form simultaneous equations

At Original speed

280=ut

Making the time t the subject t= 280/u

At new speed

280=(u+5) (t-1)

Again making time t the subject
t= 280/(u+5) +1

Set equations equal to each other

280/u = 280/(u+5) +1

Get rid of fractions by multiplying everything by denominators (u)(u+5)

(u)(u+5) (280/u) = (u)(u+5) (280/(u+5)) + (u)(u+5)
Cancel terms and simplify to get to

280(u+5) = 280u + u(u+5)

Expand and Solve

280u + 1400 = 280u + u^2 + 5u

u^2 + 5u - 1500= 0

Factorise

(u + 40 ) (u - 35)

Therefore u = -40 or 35
Speed cannot be negative as travelling to a place hence the spited has to be 40km/h