Test: Distance/Rate Problems - GMAT MCQ

To solve this problem, we need to find the time it takes for the person's hand to move 0.25 foot more than the person's shoes. We can set up a proportion to solve for the time.

The speed of the escalator is 90 feet per minute, and the speed of the handrail is 93 feet per minute. Let's assume that the time it takes for the hand to move 0.25 foot more than the shoes is t seconds.

During this time, the person's shoes will have moved a distance of 90t feet, and the person's hand (on the handrail) will have moved a distance of 93t feet.

We can set up the following equation based on the given information:

93t - 90t = 0.25

Simplifying the equation, we have:

3t = 0.25

Dividing both sides by 3, we get:

t = 0.25/3 = 0.0833...

Since the question asks for the answer in seconds, we need to convert 0.0833... minutes to seconds. There are 60 seconds in one minute, so:

0.0833... minutes * 60 seconds/minute = 5 seconds (rounded to the nearest whole number)

Therefore, the person's hand will have moved 0.25 foot more than the person's shoes in approximately 5 seconds.

The correct answer is C.

Let's assume Marcus's one-way commute time is t hours.

When Marcus drives to work at an average speed of 50 miles per hour, the distance covered is 50t miles.

When Marcus drives home from work at an average speed of 25 miles per hour, the distance covered is 25(2t) = 50t miles. (Twice the time because it takes him twice as long to drive home).

According to the given information, Marcus spends a total of 3 hours in his car for the round trip, so:

t + 2t = 3

Combining like terms, we have:

3t = 3

Dividing both sides by 3, we get:

t = 1

Therefore, Marcus's one-way commute time is 1 hour.

To find the distance of Marcus's commute one-way, we can substitute t = 1 back into one of the distance formulas:

Distance = 50t = 50(1) = 50 miles

So, Marcus's one-way commute distance is 50 miles.

The correct answer is D.