SOLUTION: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

Algebra ->  Human-and-algebraic-language -> SOLUTION: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.       Log On


   

Question 144579: Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Answer by shahid(44) About Me  (Show Source):
You can put this solution on YOUR website!
let x be his speed to cover given distance d=200miles in time t hours then
d=xt
200=xt .........(1)
if he runs 10mph faster so his speed becomes (x+10)mph and this takes 1 hour less so now time to complete this distance becomes (t-1)hour.again
d=(x+10)(t-1) by formula distance= speed*time
200=xt-x+10t-10
200=200-x+10t-10 from equ:1 xt=200
0=-x+10t-10 200 be canceled
x=10t-10 putting this in equ:1
200=(10t-10)t
200=10t^2-10t
10t^2-10t-200=0
t^2-t-20=0 taking 10 common
t^2-5t+4t-20=0
t(t-5)+4(t-5)=0
(t-5)(t+4)=0
t-5=0 i-e t=5 we neglect t+4=0 that gives negative time
putting t=5hours in equ:1
200=x(5)
x=200/5
x=40mph