Question

two trains are travelling away from a station at different speeds.

• train a is 200 miles from the station and traveling at a rate of 100 mph.
• train b is 600 miles from the station and traveling at a rate of 80 mph.

the following system of equations models the two trains.
$m = 100h + 200$
$m = 80h + 600$
find the solution to the system to determine how many hours, $h$, after leaving the station the two trains will be the same number of miles, $m$, from the station.
\boxed{} hours after leaving the station both trains will be \boxed{} miles from the station.

Explanation:

Step1: Set the equations equal

Since both equal \( m \), set \( 100h + 200 = 80h + 600 \).

Step2: Solve for \( h \)

Subtract \( 80h \): \( 20h + 200 = 600 \).
Subtract 200: \( 20h = 400 \).
Divide by 20: \( h = 20 \).

Step3: Find \( m \)

Substitute \( h = 20 \) into \( m = 100h + 200 \):
\( m = 100(20) + 200 = 2000 + 200 = 2200 \).

Answer:

20 hours after leaving the station both trains will be 2200 miles from the station.