Distance, Speed, and Time John and Mary leave their house at...

Distance, Speed, and Time John and Mary leave their house at the same time and drive in opposite directions. John drives at 60 mi/h and travels 35 mi farther than Mary, who drives at 40 $\mathrm{mi} / \mathrm{h}$ . Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?

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Key Concepts

Relative Motion

Relative motion deals with the analysis of how objects move in relation to each other. In cases where multiple objects depart from the same point or in opposite directions, the concept helps in setting up equations based on how distances and times are interrelated.

Unit Conversions

Often in problems involving time, distance, and speed, different units (such as minutes and hours) are used. Converting all measurements into consistent units is crucial to ensure that the calculations are accurate.

Systems of Equations

When multiple unknowns interact under several conditions, systems of equations are used to express the relationships between them. In problems like these, each condition provides an equation, and solving the system gives the values of the unknown variables.

Distance-Speed-Time Relationship

This is a fundamental concept in physics and mathematics which relates distance, speed, and time through the equation d = vt. It is essential in solving problems where any two of these variables are known and the third variable is to be determined.

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