# word problemm

#### really lost

##### New member
:?
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

#### tkhunny

##### Moderator
Staff member
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

##### Elite Member
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

##### New member
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

Staff member