Monica is currently 400 miles from home and is traveling 50 mph. her sister marcia is 300 miles from home and is traveling at a rate of 30 mph. at what time will monica and marcia be at the same distance from home? what is the distance?

This assumes that the 2 girls are traveling in the same direction!  Are they traveling FROM Home or TO Home?  Gotta figure that out.

If FROM Home:

Monica's trip is defined by Mon(t) = 400 mi + (50 mph)t, and

Marcia's trip is defined by Mar(t) = 300 mi + (30 mph)t

We must set these equal to one another and try to solve for time, t:

400+50t = 300+30t                then 100= -20t.  This results in a negative time answer, which is not possible.  

Therefore, we must assume that the 2 girls are traveling TO Home.

Monica's trip is defined by Mon(t) = 400 mi - (50 mph)t, and

Marcia's trip is defined by Mar(t) = 300 mi - (30 mph)t

When do they meet?  Solve 400 - 50t = 300 - 30t

100 = 20t, and t = 5 hours (answer)

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