A mountain rescue snowmobile is dispatched to retrieve a stranded hiker. It travels from b… — Armed Services Vocational Aptitude Battery (ASVAB)

A mountain rescue snowmobile is dispatched to retrieve a stranded hiker. It travels from base camp to the hiker's location at an average speed of $30$ miles per hour. Carrying the extra passenger on the return trip, the snowmobile heads back along the exact same trail at an average speed of $20$ miles per hour. If the total driving time for the entire rescue mission is $90$ minutes, what is the total round-trip distance traveled by the snowmobile?

A
$18$ miles
$36$ milesCevap
C
$37.5$ miles
D
$75$ miles

Cevap

The total round-trip distance is

36

miles.

To find the total distance, we must use the relationship between distance, rate, and time. Because the one-way distances are equal, we can represent the one-way distance as

d

. The time for the outbound trip is

\frac{d}{30}

and the return trip is

\frac{d}{20}

. Their sum equals the total time of

1.5

hours (since

90

minutes is

1.5

hours). Solving

\frac{d}{30} + \frac{d}{20} = 1.5

yields

d = 18

. The round-trip distance is

2d

, which is

36

miles.

Adım Adım Çözüm

Convert the total driving time from minutes to hours.

90 \text{ minutes} = 1.5 \text{ hours}

Speed is given in miles per hour, so time must be consistent with these units.

Set up an equation representing the total time using the formula

\text{Time} = \frac{\text{Distance}}{\text{Rate}}

. Let

d

represent the one-way distance.

\frac{d}{30} + \frac{d}{20} = 1.5

The total time is the sum of the time taken for the outbound trip and the time taken for the return trip.

Solve for the one-way distance (

d

) by finding a common denominator.

\frac{2d}{60} + \frac{3d}{60} = 1.5 \Rightarrow \frac{5d}{60} = 1.5 \Rightarrow \frac{d}{12} = 1.5 \Rightarrow d = 18 \text{ miles}

Solving the equation provides the distance for a single leg of the journey.

Calculate the total round-trip distance by multiplying the one-way distance by 2.

18 \times 2 = 36 \text{ miles}

The question asks for the total round-trip distance, which includes both the outbound and return legs.

Anahtar Kavram

Calculating distance for a round trip involving different speeds by setting up a total time equation.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru