Modeling with Equations Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Two trains leave the same station traveling in opposite directions at 50 mph and 70 mph. After how many hours are they 360 miles apart?

Solution

  1. 1
    Combined speed: 50+70=12050 + 70 = 120 mph (moving apart).
  2. 2
    Distance apart after tt hours: 120t=360120t = 360.
  3. 3
    Solve: t=3t = 3 hours.

Answer

t=3 hourst = 3 \text{ hours}
When objects move in opposite directions, their speeds add. Setting up the equation requires identifying the relationship: distance = rate × time.

About Modeling with Equations

Translating a real-world situation into one or more equations that capture its mathematical relationships and constraints.

Learn more about Modeling with Equations →

More Modeling with Equations Examples

Example 1 easy

A phone plan costs [formula]0.10 per text. Write an equation for the monthly cost [formula] if you s

Example 3 easy

Write an equation: 'A number doubled and increased by 7 equals 25.'

Example 4 hard

The sum of three consecutive integers is 72. Find them.

← All Modeling with Equations Examples Modeling with Equations Concept