SOLUTION: Here's my question: A train leaves Newcastle for Sydney at 7:45am while another train leaves from Sydney for Newcastle at 8:15am. The first train arrives in Sydney 40 minutes af

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Question 998290: Here's my question:
A train leaves Newcastle for Sydney at 7:45am while another train leaves from Sydney for Newcastle at 8:15am. The first train arrives in Sydney 40 minutes after the trains pass each other while the train to Newcastle arrives 1 hour 40 minutes after they pass. Assume that the trains travel at a constant speed, let t be the time, in mins, that takes the first train to meet the second train. Find the time that takes the second train to meet the first train in terms of t. Find the value of t.
Thank you in advance! :D
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A train leaves Newcastle for Sydney at 7:45am while another train leaves from Sydney for Newcastle at 8:15am.
The first train arrives in Sydney 40 minutes after the trains pass each other while the train to Newcastle arrives 1 hour 40 minutes after they pass.
Assume that the trains travel at a constant speed, let t be the time, in mins, that takes the first train to meet the second train.
Find the time that takes the second train to meet the first train in terms of t.
:
Train 2 started a half hour after train 1, therefore
t - 30 = train 2's time to the meeting point
:
:
Find the value of t.
A diagram will help to understand this, they meet at *
Change 1 hr 40 min to 100 min
:
Train 1; N.C >---------t--------->*>------40------> Sydney
Train 2: N.C <--------100-------<*<---(t-30)-----< Sydney
:
Write a time relationship between the two trains for same distances
=
cross multiply
t(t-30) = 100 * 40
t^2 - 30t = 4000
A quadratic equation
t^2 - 30t - 4000 = 0
This will factor to
(t-80)(t+50) = 0
the positive solution is what we want here
t = 80 minutes