SOLUTION: At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the w

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the w      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 638020: At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the way, and it was revealed that the hiker from city B to city A traveled two km more than the other hiker. This hiker arrived to city A 40 minutes after the two met, and the hiker from city A arrived to city B an hour and a half after they met. What is the distance of the trail?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At the same time, two hikers took off, one from city B to city A and the other
from city A to city B.
They hiked the same distance and their speeds were constant.
They met on the way, and it was revealed that the hiker from city B to city A
traveled two km more than the other hiker.
This hiker arrived to city A 40 minutes after the two met, and the hiker from
city A arrived to city B an hour and a half after they met.
What is the distance
:
Do this using minutes for the time
let t = travel time to the point where they met
:
let x = dist from A to the meeting point
and
(x+2) = dist from B to the meeting point
then
x + (x+2) = 2x+2 km is the distance from A to B
:
A<-----40min------*---------t min-------< B(hiker B's path)
A------x km-------*-------(x+2)km-------B
A>-----t Min------*--------90min--------> B (hiker A's path)
:
Hiker B,
t%2F40 = %28%28x%2B2%29%29%2Fx
Cross multiply
tx = 40(x+2)
tx = 40x + 80
t = %2840x%2B80%29%2Fx
:
Hiker A
t%2F90 = x%2F%28x%2B2%29
Cross multiply
t(x+2) = 90x
t = %2890x%29%2F%28x%2B2%29
:
t=t, therefore:
%2890x%29%2F%28x%2B2%29 = %2840x%2B80%29%2Fx
Cross multiply
90x^2 = (x+2)(40x+80)
FOIL
90x^2 = 40x^2 + 80x + 80x + 160
90x^2 = 40x^2 + 160x + 160
Combine on the left
90x^2 - 40x^2 - 160x - 160 = 0
50x^2 - 160x - 160 = 0
Simplify, divide by 10
5x^2 - 16x - 16 = 0
Factors to
(5x + 4)(x - 4) =
The positive solution is all we want here
x = 4
"What is the distance?"
2(4) + 2 = 10 km is the distance from A to B
:
:
Confirm this, find t
t = %2890%2A4%29%2F%284%2B2%29
t = 60 min
Find the speed of A & B
A's time in hrs (90+60)/60 = 2.5 hrs
A's speed 10/2.5 = 4 km/hr
and
B's time in hrs (40+60)/60 = 12%2F3 hrs
A's speed 10/1.67 ~ 6 km/hr
:
Find how far each traveled in 1 hr (t)
B: 6 km
A: 4 km
---------
dif: 2 km