Two cyclists, Sarah and Mike, start at opposite ends of a 60-mile trail and ride directly … — Armed Services Vocational Aptitude Battery (ASVAB)

Two cyclists, Sarah and Mike, start at opposite ends of a $60$ -mile trail and ride directly toward each other. Sarah rides at a constant speed of $12$ mph, and Mike rides at a constant speed of $18$ mph. How many hours will it take for them to meet?

Answer: 2 hours

Answer

Because the cyclists are moving directly toward each other, their gap closes at a combined rate of

30

mph (

12

mph +

18

mph). Dividing the total initial distance of

60

miles by this combined rate yields exactly

2

hours.

Step-by-Step Solution

Calculate the combined relative speed.

30 mph

When objects move toward each other from opposite directions, their relative speed is the sum of their individual speeds (

12 + 18 = 30

Calculate the time required to meet.

2 hours

Using the formula Time = Distance / Rate, divide the total distance (

60

miles) by the relative speed (

30

mph).

Key Concept

Relative Motion and Catch-Up Scenarios

Question

Answer

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Key Concept

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