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
