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