SOLUTION: I am having trouble comming up with an an equation to solve the following problem. Please help. In a certain number of hours a man traveled 36 Km. If he had travelled 1.5 Km/h f

Algebra ->  Equations -> SOLUTION: I am having trouble comming up with an an equation to solve the following problem. Please help. In a certain number of hours a man traveled 36 Km. If he had travelled 1.5 Km/h f      Log On


   

Question 427172: I am having trouble comming up with an an equation to solve the following problem. Please help.
In a certain number of hours a man traveled 36 Km. If he had travelled 1.5 Km/h faster, it would have taken 3 hours less to make the journey How many kiometers did he travel per hour.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I am having trouble comming up with an an equation to solve the following problem. Please help.
In a certain number of hours a man traveled 36 Km. If he had travelled 1.5 Km/h faster, it would have taken 3 hours less to make the journey How many kilometers did he travel per hour.
..
let x=initial speed
x+1.5=if speed
travel time=distance/speed
initial travel time=36/x
if travel time=36/x+1.5
difference in travel times=3=initial-if travel times
3=36/x-36/x+1.5
LCD=x(x+1.5)
36(x+1.5)-36x=3x(x+1.5)
36x+54-36x=3x^2+4.5x
54=3x^2+4.5x
3x^2+4.5x-54=0
x^2+1.5x-18=0
solve by following quadratic equation:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
..
a=1, b=1.5, c=-18
x=[-1.5+-sqrt(1.5^2-4*1*-18)]/2

x =[-1.5+-sqrt(75)]/2=(1.5+-8.66)/2=5.08 or -3.58(reject)

during initial journey he traveled 5.08 kilometers/hr