A service technician travels by boat from Pier 1 to an offshore platform at a constant spe… — GMAT

A service technician travels by boat from Pier 1 to an offshore platform at a constant speed of $30$ miles per hour. Immediately upon arrival, the technician returns along the exact same route to Pier 1 at a constant speed of $60$ miles per hour. If the entire round-trip journey takes $3$ hours, what is the total distance, in miles, traveled by the technician?

A
$60$
B
$90$
$120$ Answer
D
$135$
E
$180$

Answer

120 miles

To find the total distance, we must account for the time spent on each leg. Letting

d

be the one-way distance, the outbound time is

\frac{d}{30}

and the return time is

\frac{d}{60}

. Summing these gives

\frac{d}{30} + \frac{d}{60} = 3

hours, which simplifies to

\frac{3d}{60} = 3

, leading to

d = 60

miles. Since the technician completes a round trip, the total distance traveled is

2 \times 60 = 120

miles.

Step-by-Step Solution

Define variables for distance and express travel times for each leg of the trip.

Let

d

be the one-way distance between Pier 1 and the offshore platform. Time to reach platform:

t_1 = \frac{d}{30}

hours. Time to return:

t_2 = \frac{d}{60}

hours.

Time equals distance divided by speed (

t = \frac{d}{v}

Set up an equation using total time.

t_1 + t_2 = \frac{d}{30} + \frac{d}{60} = 3

The total duration for both legs combined is given as

3

hours.

Solve for the one-way distance

d

Find a common denominator:

\frac{2d}{60} + \frac{d}{60} = \frac{3d}{60} = \frac{d}{20} = 3 \implies d = 60

miles.

Combining fractional terms allows isolated calculation of the one-way distance.

Calculate the total round-trip distance.

Total distance

= 2d = 2 \times 60 = 120

miles.

The question specifically asks for the total distance traveled during the entire round trip.

Key Concept

Average Speed and Total Distance in Round-Trip Scenarios

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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