GRE® Quant Questionbank | Rates

Concepts Tested in Speed Distance Time

One can expect about two questions in the GRE general test - quant section from rates - speed distance time and work time. The following concepts are tested from rates in the GRE General test.

• Compute distance, speed, or time
• Relative speed between two or more objects
• Average speed of travel
• Boats in streams, aircraft with tailwind
• Races in a straight line
• Races around a circular track

Concepts Tested in Work Time

If you have understood the basics of speed, distance, and time well, solving questions from work and time becomes easy. The core concept between the two topics is the same. The way the questions are worded is the main difference between these two topics.

• Time taken to fill a tank by two or more pipes
• Ratio of time taken by two pipes of different dimensions to fill a tank
• Time taken to complete a task by two or more people or machines
• Share of wages in the ratio of work done
• Word problems in work and time

1. A and B together complete a work in 4 days, B and C together in 6 days, C and A together in 5 days. Working independently, who will finish the work in the least time and in how many days?

   1. A, \\frac{120}{7}) days
   2. A, \\frac{120}{17}) days
   3. B, \\frac{120}{13}) days
   4. B, \\frac{120}{17}) days
   5. C, \\frac{120}{7}) days

   Correct AnswerChoice B
   A, \\frac{120}{17}) days

   Explanation Video Solution
   Approach to solve this Work Time Word Problem

   Step 1: Assign three variables - one each for the fraction of work done by A, B, and C respectively in a day.
   Step 2: Frame three equations for fraction of work done A, B, and C taking two at a time as mentioned in the question stem.
   Step 3: Solve the three equations to find the values for the fraction of work done by each of A, B, and C in a day.
   Step 4: The person who does the highest fraction of work in a day is the most efficient and the fastest.
   Step 5: The reciprocal of the fraction of the work done in a day by that person is the least time taken to complete the task.
   

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2. Sam covers the first 40% of the distance between two cities A and B at 50 kmph and the remaining distance at a speed of 75 kmph. What is his average speed for the entire travel?

   1. 62.5 kmph
   2. 65 kmph
   3. 60 kmph
   4. 66.66 kmph
   5. 58.33 kmph

   Correct AnswerChoice A
   62.5mph

   Explanation Video Solution
   Approach to solve this GRE Average Speed Question

   Step 1: Assume a value for 40% of the distance and consequently derive the remaining distance. A good number to assume for 40% of the distance is the LCM of the two speeds viz., 50 and 75.
   Step 2: Add the distances of the two parts to compute the total distance covered by Sam
   Step 3: Find out time taken to cover the two parts. Add the two values to compute the total time taken.
   Step 4: Compute average speed. Average speed formula = \\frac{\text{Total Distance}}{\text{Total Time}})

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3. Ron, Sid, and Tom plan to leave city A by 3 cars towards a farmhouse along the same route. Ron travels at 50 mph, Sid at 60 mph. Sid leaves 2 hours after Ron and they reach the farmhouse at the same time. If Tom plans to drive at 80 mph, how long after Sid should Tom leave city A if he wishes to reach the farmhouse at the same time as Ron and Sid.

   1. 1 hr
   2. 90 min
   3. 3 hrs
   4. 150 min
   5. 4.5 hrs

   Correct AnswerChoice D
   150 minutes

   Explanation Video Solution
   Approach to solve this GRE Speed Distance Question

   Concept: Distance travelled by Ron, Sid, and Tom is the same. Equate distances travelled by them.
   Step 1: Assign a variable for the time taken by Ron to reach the farmhouse. Say, Ron takes t hours. Compute distance travelled by Ron.
   Step 2: Because Sid starts 2 hours after Ron, Sid will take (t - 2) hours. Compute distance travelled by Sid.
   Step 3: Equate distances covered by Ron and Sid and compute 't' and the distance travelled by them.
   Step 4: From distance computed in step 3, compute time taken by Tom to reach farmhouse. Compute answer to the question.

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4. If machine A polishes x units in 12 minutes and machine B polishes 5x units in 40 minutes, in how many minutes will A and B, working together, polish 50x units.

   Correct Answer240 minutes
   

   Explanation Video Solution
   Approach to solve this GRE Numeric Entry Question

   Step 1: Compute number of units polished by Machine A in 1 minute. The answer will contain 'x'
   Step 2: Compute number of units polished by Machine B in 1 minute. The answer will contain x.
   Step 3: Compute number units that Machines A and B can polish in 1 minute by adding information in steps 1 and 2. The answer will be in terms of x.
   Step 4: Divide 50x by the expression obtained in step 3 to find the time taken when the machines work together to polish 50x units. The answer will be in minutes.

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5. P and Q take 4 hours to complete a task. P, Q, and R take 2 hours to complete the task.

   Quantity A	Quantity B
   Time taken by P alone to complete the task.	Time taken by R alone to complete the task.

   1. Quantity A is greater
   2. Quantity B is greater
   3. The two quantities are equal
   4. Cannot be determined

   Correct AnswerChoice A
   

   Explanation Video Solution
   Approach to solve this GRE Quantitative Comparison Question

   Question Stem: Let P, Q, and R take P hours, Q hours, R hours when they work independently.
   Step 1: So, P will complete \\frac{1}{P}) of the task in an hour. Q will complete \\frac{1}{Q}) of the task and R will complete \\frac{1}{R}) of the task in an hour.
   Step 2: Frame equation when P and Q work together. Frame equation when all 3 work together.
   Step 3: Solve the two equations to compute the value of R. This is the answer for Quantity B.
   Step 4: Understand what range of values P can take by comparing time taken by R and time taken by P and Q.
   Step 5: Compare two quantities and arrive at the answer.
   

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