Question

a man walks A certain distance with certain speed if he walks 1/2 half kilometre an hour faster he takes 1 hours less but if he walks 1 km an hour slower it is 3 more hours find the distance covered by the man and his original rate of

Answer 1

let distance be d km
usual speed be x km /hr
and time be t hours

now ,

if x+1/2 then t-1

ie. d= (x+1/2) × ( t-1) -----(1)

and

if x-1 then t+3

ie. d= (x-1) × ( t+3) -----(2)


from 1 and 2

(x-1) × ( t+3) = (x+1/2) × ( t-1)

xt +3x -t -3 = xt -x +1/2t -1/2


3x + x = t + 1/2t +3 -1/2

4x = 3/2t + 5/2

8x = 3t+5

by putting some values and trial and error

we get

x = 2.5 km /hr

t = 5 hours

d = 12.5 km