SOLUTION: an express train and local train leave vancouver at 3pm and head for hope 180 kms away. the local train travels two thirds as fast as the express train and arrives 1 hour after the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: an express train and local train leave vancouver at 3pm and head for hope 180 kms away. the local train travels two thirds as fast as the express train and arrives 1 hour after the      Log On


   

Question 536196: an express train and local train leave vancouver at 3pm and head for hope 180 kms away. the local train travels two thirds as fast as the express train and arrives 1 hour after the express train. what time does thelocal train arrive in hope?
i have so far
LOCAL: D = R x T
180=2/3R x T+1
EXPRESS: D = R x T
180= R x T
LOCAL: T=180/ 2/3r -1
EXPRESS; T=180/R
I DONT KNOW WHAT THE LCM IS FOR 2/3R AND R ...IS IT 1 2/3 R ? OR r(2/3r)>?<


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = hours it takes local train to get to Hope
+t+-+1+ = hours it takes express train to get to Hope
Let s = the speed of the fast train in km/hr
+%282%2F3%29%2Af+ = speed of the local train in km/hr
-----------
For local train:
(1) +180+=+%282%2F3%29%2As%2At+
For express train:
(2) +180+=+s%2A%28+t+-+1+%29+
-----------------
(1) +540+=+2%2As%2At+
(1) +s%2At+=+270+
and
(2) +180+=+s%2At+-+s+
Substitute (1) into (2)
(2) +180+=+270+-+s+
(2) +s+=+90+
and
(1) +s%2At+=+270+
{1) +t+=+270%2F90+
(1) +t+=+3+
The local train arrives at 3 PM + 3 hrs = 6 PM
check:
(1) +180+=+%282%2F3%29%2A90%2A3+
(1) +180+=+180+
OK