word problemm

really lost

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an express and local train leave grayslake at 3pm and head for chicago 50 miles away. the express travels twice as fast as the local and arrives 1 hr ahead of the local. find the speed of each train







please help this is so confusing
 

tkhunny

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really lost said:
an express and local train leave grayslake at 3pm and head for chicago 50 miles away. the express travels twice as fast as the local and arrives 1 hr ahead of the local. find the speed of each train
Name stuff!

E = Speed of Express Train
L = Speed of Local Train

Distance = Rate * Time
Distance = 50 mi

Express Train:

50 miles = Rate<sub>e</sub>*Time<sub>e</sub>

Local Train:

50 miles = Rate<sub>l</sub>*Time<sub>l</sub>

the express travels twice as fast as the local

Rate<sub>e</sub> = 2*Rate<sub>l</sub>

Express Train:

50 miles = (2*Rate<sub>l</sub>)*Time<sub>e</sub>

Local Train:

50 miles = Rate<sub>l</sub>*Time<sub>l</sub>

the express ... arrives 1 hr ahead of the local

Time<sub>e</sub> = Time<sub>l</sub> - 1 hr

Express Train:

50 miles = 2*Rate<sub>l</sub>*(Time<sub>l</sub> - 1 hr)

Local Train:

50 miles = Rate<sub>l</sub>*Time<sub>l</sub>

Just one piece at a time. Don't be afraid to write each step and record each observation.

Can you finish from there?
 

soroban

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Jan 28, 2005
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Hello, really lost!

An express and local train leave Grayslake at 3pm and head for Chicago 50 miles away.
The express travels twice as fast as the local and arrives 1 hr ahead of the local.
Find the speed of each train.
You're expected to know: . Distance = Speed x Time

. . and its variation: . Time = Distance/ Speed


Let x be the speed of the local (in miles per hour).
Let 2x be the speed of the express (in miles per hour).

The local travels 50 miles at x mph. .It takes 50/x hours

The express travels 50 miles at 2x mph. .It takes 50/2x = 25/x hours.


The express's time is one hour less than the local's time:

. . . .25 . . . . 50
. . . ---- . = . ---- - 1
. . . . x . . . . . x


Multiply through by x: . 25 .= .50 - x . . ---> . . x .= .25

Therefore: . speed of local is 25 mph
. . . . . . . . . . speed of express is 50 mph

Edit: Too fast for me, TK!
 

really lost

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Jul 19, 2005
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thankyouuuuu

:) thanks its just sooo confusing for me to figure out a speed when there isnt one given but i have to stop thinking about it and try to remember the formulas for my test
 

tkhunny

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Right! Let the notation help you think. Don't try to cram it all in your head at the same time.
 
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