Question

Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the other train travels at 80 mph. How much times passes until the trains are 600 mi apart?

Question 4 options:

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5

Answer 1

I assume the units are hours.

If one train travels 70mph, and the other travels 80mph in the opposite direction, then after 1 hour, their distance is 70(1) + 80(1)
After 2 hours, their distance is 70(2) + 80(2)

Notice a pattern?
We can model their total distance as 70x + 80x where x is the number of hours.

So to put it in an equation:
600 miles = 70x + 80x

Can you solve for x?

Answer 2

x=4m?

Answer 3

@mhchen

Answer 4

Not 4 miles, 4 hours. x is in hours.

Answer 5

I don't seem to understand... :/

Answer 6

Okay so. Distance = speed * time right?
The distance that one of the train travels is 70 miles every hour.
The distance that the other train travels is 80 miles every hour.
That is their SPEED.

Now to find the DISTANCE they travel, you MULTIPLY their SPEED by TIME.
But since we are solving for time, we substitute time as x:
(70mph) * (x hours) = 70*x miles.
(80mph) * (x hours) = 80*x miles.

Since they are going in opposite directions, the distance between them is just adding up the distance they've travelled.

That's why we have our equation of
70x + 80x = 600
\[(\frac{ 70 miles }{1 hour }*\frac{ xhours }{1}) + (\frac{ 80 miles }{1 hour }*\frac{ xhours }{1}) = 600\]

We can simplify that equation to

\[(70*x) miles + (80*x)miles = 600\]

So then we add up the left side:
\[(150*x)miles = 600miles\]

Divide:
\[x = \frac{ 600miles }{ (150)miles }\]

And the x would be the hours.

Answer 7

600/(150)= 4