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Test: Distance/Rate Problems - GMAT MCQ


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10 Questions MCQ Test - Test: Distance/Rate Problems

Test: Distance/Rate Problems for GMAT 2024 is part of GMAT preparation. The Test: Distance/Rate Problems questions and answers have been prepared according to the GMAT exam syllabus.The Test: Distance/Rate Problems MCQs are made for GMAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Distance/Rate Problems below.
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Test: Distance/Rate Problems - Question 1

An escalator installed at a new shopping mall operates at a speed of 90 feet per minute. The handrail of the escalator operates on a separate motor at a speed of 93 feet per minute. A person steps onto the escalator and, at the same time, grabs the handrail. Assuming that the person's hand and shoes do not move on the escalator in how many seconds will the person's hand have moved 0.25 foot more than the person's shoes?

Detailed Solution for Test: Distance/Rate Problems - Question 1

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.

Test: Distance/Rate Problems - Question 2

Due to rush hour traffic, it takes Marcus twice as long to drive home from work as it does for him to drive to work. When he drives to work, his average speed is 50 miles per hour. When he drives home from work, his average speed is 25 miles per hour. If he spends a total of three hours in his car driving to and from work, how long is Marcus's commute one-way?

Detailed Solution for Test: Distance/Rate Problems - Question 2

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.

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Test: Distance/Rate Problems - Question 3

Phil drives east from his home for 2 hours before realizing that he will run out of fuel in another 70 miles. Nevertheless, he drives for another 10 miles east before returning back home via the same route. If he drives at a constant speed throughout his journey and returns home with fuel left for another 10 miles, how much time does he take for his journey eastwards?

Test: Distance/Rate Problems - Question 4

Ahmad drives from his house to his friend's house averaging 60 miles per hour. On the return trip, he averages 50 miles per hour. His total driving time is 11 hours. What is the distance, in miles, between Ahmad's house and his friend`s house?

Test: Distance/Rate Problems - Question 5

If John travels to his school from his home at 2 km/hr he will be 15 minutes late. If he travels at 5 km/hr he will be 30 minutes early. Find the distance from his home to the school.

Test: Distance/Rate Problems - Question 6

Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

Test: Distance/Rate Problems - Question 7

John drives from Rome to Paris at 50mph on a particular route, and returns along the exact same route at 60mph. What is his average speed for the trip?

Test: Distance/Rate Problems - Question 8

Shelby drives her scooter at a speed of 30 miles per hour if it is not raining, and 20 miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of 16 miles in 40 minutes. How many minutes did she drive in the rain?

Test: Distance/Rate Problems - Question 9

A jeep travels a distance of 100 km at a uniform speed. If the speed of the jeep is 5 kmph more, then it takes 1 hour less to cover the same distance. The original speed of the jeep is

Test: Distance/Rate Problems - Question 10

An athlete is riding his bicycle along the boundaries of a square field starting from the corner point A. He reaches the corner point C located diagonally opposite to the starting point after riding for 30 minutes. If the speed of the athelete's bicycle is 8 km per hour, then what is the area of the field in square kilometers?

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