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

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
RELATED QUESTIONS
A car travels from Sydney to Newcastle and back to Sydney of a total of 310km in 4.0h.... (answered by greenestamps)

One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New (answered by bucky)

A ship leaves Sydney and travels due north for two hours at 24km/h, it then travels due... (answered by ankor@dixie-net.com)

A car left Melbourne For Sydney at 12:30 pm and travelled at an average speed of 80km/h. (answered by josgarithmetic)

My question is: A train leaves Chicago traveling west at 60 miles per hour.An hour later (answered by josgarithmetic,rothauserc)

Note: My teacher says that the distance between Santa Fe and Topeka is not a factor in... (answered by Stitch)

At noon, a train leaves New York for Toronto while another train leaves Toronto for New... (answered by ptfile,MathTherapy)

Train one leaves from station A towards station B at a speed of 50 km/hr . Train two... (answered by richwmiller)

If a train leaves new york at 35mph and another train leaves millwaukee st 30mph where... (answered by Alan3354)