A dispatch rider is transporting urgent documents between two military installations. The … — Armed Services Vocational Aptitude Battery (ASVAB)

A dispatch rider is transporting urgent documents between two military installations. The rider travels on a paved highway at a constant speed of $65\text{ mph}$ for $1\text{ hour and } 12\text{ minutes}$ . Upon reaching a rural sector, the rider continues on an unpaved route at a steady speed of $42\text{ mph}$ for $35\text{ minutes}$ . What is the total distance, in miles, the dispatch rider traveled?

Answer: 102.5 miles

Answer

102.5

To find the total distance, calculate the distance for each leg of the trip separately by ensuring time is expressed in hours. For the first leg,

1\text{ hour and } 12\text{ minutes}

1.2\text{ hours}

. Multiplying the

65\text{ mph}

rate by

1.2\text{ hours}

gives

78\text{ miles}

. For the second leg,

35\text{ minutes}

\frac{35}{60}

\frac{7}{12}\text{ of an hour}

. Multiplying the

42\text{ mph}

rate by

\frac{7}{12}\text{ hours}

gives

24.5\text{ miles}

. Adding these two distances together (

78 + 24.5

) gives a total of

102.5\text{ miles}

Step-by-Step Solution

Convert the highway travel time into hours.

1\text{ hour and } 12\text{ minutes} = 1 + \frac{12}{60}\text{ hours} = 1.2\text{ hours}

The speed is given in miles per hour, so time must be converted to hours to match units.

Calculate the distance traveled on the highway.

65\text{ mph} \times 1.2\text{ hours} = 78\text{ miles}

Applying the formula: Distance = Rate

\times

Time.

Convert the unpaved route travel time into hours.

35\text{ minutes} = \frac{35}{60}\text{ hours} = \frac{7}{12}\text{ hours}

Time must be in hours for consistency with the speed unit.

Calculate the distance traveled on the unpaved route.

42\text{ mph} \times \frac{7}{12}\text{ hours} = 24.5\text{ miles}

Applying the formula: Distance = Rate

\times

Time.

Calculate the total distance.

78\text{ miles} + 24.5\text{ miles} = 102.5\text{ miles}

The total journey distance is the sum of the individual distances from each leg.

Key Concept

Calculating total distance for a multi-leg journey by accurately converting fractional times to hours and applying the distance formula.

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