The two kinds of MCQ questions in the quantitative reasoning section are- data sufficiency and problem-solving. The quantitative section of the paper requires basic knowledge of elementary algebra, arithmetic and certain concepts of geometry. While every topic is equally important in the quantitative section, here we will discuss time and distance questions for GMAT. These questions are slightly difficult and need to be approached with proper formulas and understanding. Let us first explore some tips and examples of the time and distance questions for GMAT that will come into play while preparing for the examination.
Also Read: GMAT Syllabus 2021 [Updated Version]
This Blog Includes:
- Understanding Time and Distance Questions
- What is a Distance/Speed/Time Word Problem?
- General Tips for Time and Distance Questions
- Solved Examples of Time and Distance Questions for GMAT
- Time and Distance Questions: More Practice Questions
- Time and Distance Questions Worksheet
- Time, Distance and Speed Conversions
Understanding Time and Distance Questions
Time and distance questions are basically based on the simple formula:
Speed= Distance/ Time
This formula might appear simple but if your basic concept is not clear, it may result in a wrong answer. This may furthermore result in losing a valuable amount of time. So, let us approach the time and distance questions focusing on different concepts.
Average Speed
Average speed refers to the total distance travelled divided by the total time taken to travel the distance. This is mathematically written as,
Avg S= TD/TT
Where S= Speed
TD= Total Distance
TT= Total Time
Also Read: Everything about GMAT Exam : Syllabus,Preperation,Fees
What is a Distance/Speed/Time Word Problem?
- There is usually something or someone moving at a steady or average speed.
- We are asked to find one of the three quantities (speed, distance, and time).
- In the query stem, you’ll find details about the other two.
General Tips for Time and Distance Questions
Let us look at some general tips you need to keep in mind while attempting the GMAT paper. Following are the major strategies that you can incorporate when practicing:
- Make a preferred section choice in order before attempting the actual choice GMAT exam.
- Use the time allotted wisely.
- Thoroughly read the directions given in the test.
- Practise and revise all the different kinds of questions before the examination.
- Do not spend too much time on a single question.
- Read every question thoroughly.
- Your essay answer should be well prepared before you write it in the GMAT exam.
- Revise your answers before submission.
Also Read: Statistics Formulas for GMAT Quantitative Section
Solved Examples of Time and Distance Questions for GMAT
Q. A man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
Solution: Let us understand how we can calculate it-
Let the time in which he travelled on foot=x hr
Then the time in which he travelled on bicycle
=(9−x)=(9−x)hr
distance = speed × time
⇒4x+9(9−x)=61
⇒4x+81−9x=61
⇒5x=20
x=4
⇒4x+9(9−x)=61⇒4x+81−9x=61⇒5x=20⇒x=4
Distance traveled on foot
=4x
=4×4=16 km
=4x=4×4=16 km
Q. A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
Solution: Let us now see how we can solve this –
Distance from A and B be ‘d’
Average Speed = total distance / total time
Average Speed = (2d) / [(d/20) + (d/30)]= (2d) / [5d/60) => 24 kmph
Q. By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Solution: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km
He covered 2/3 x 120x = 80x km in 1/3 x 3x = x hours
So, the remaining 40x km, he has to cover in 2x hours would be required speed = 40x / 2x = 20 kmph
Q. To qualify for a race, you must drive two laps around a one-mile track at an average speed of 60 mph. You have an engine problem on the first lap, and you only average 30 mph; how hard do you have to drive the second lap to average 60 mph for both of them?
Solution: Let’s begin with a problem that has already been discussed. You’ll notice that by explicitly listing the data in tabular form, we remove any potential for misunderstanding.
Distance in miles | Average speed in mph | Time in hours | |
LAP 1 | 1 | 30 | 1/30 |
LAP 2 | 1 | y | 1/y |
TOTAL | 2 | 60 | 1/30 |
LAP 1:
Time = Distance/Speed = 1/30
LAP 2:
Time = Distance/Speed = 1/y
TOTAL:
Time = Distance/Speed = 2/60 = 1/30
Also, the cumulative time should be equal to the number of the times in rows 1 and 2. As a result, we can derive the following equation.
Total Time = Time (LAP 1) + Time (LAP 2)
1/30 = 1/30 + 1/y
1/y= 1/30 – 1/30 = 0
Hence, there can be no speed for which the average can be made up in the second lap because ‘y’ is the reciprocal of 0, which does not exist.
Also Read: GMAT Verbal Reasoning Questions Explained!
Time and Distance Questions: More Practice Questions
Q. A train travelling at 200kmph overtakes a car at 74kmph in 1 minute. What is the length of the train mentioned in the question?
- 1800 meters
- 1822 meters
- 1200 meters
- 500 meters
Q. Aditya travels the first 4 hours at 50mph speed and the remaining 6 hours at 25mph. Calculate the average speed of Aditya in mph.
- 50mph
- 46mph
- 52.5mph
- 62.4mph
Q. Yash covered a distance of 350 miles between City A and City B, taking a total of 8 hours. If a part of the journey was covered at 50 miles per hour speed and the balance at 90mph speed, how many hours did she travel at 50 miles per hour?
- 3 hours 20 minutes
- 5 hours
- 4 hours
- 2 hour 55 minutes
Q. Altamash travelled the first 3 hours of his journey at 40mph, and the last 5 hours of his journey at 60mph. What is the average speed of travel for the entire journey?
- 90 mph
- 86.68 mph
- 97.55 mph
- 84mph
Q. Jay flies at 60 mph for the first 3 hours of his trip and 24 mph for the remaining 5 hours. In mph, what is Jay’s average travel speed?
- 37.5 mph
- 42.5 mph
- 48 mph
- 42 mph
- 36 mph
Q. Sam is 25% quicker than Peter and is able to give Peter a 7-meter lead to end the race in a dead heat. What is the race’s duration?
- 45 meters
- 15 meters
- 10 meters
- 25 meters
- 35 meters
Q. When an individual walks at 4 miles per hour, he covers a certain amount of ground. He can cover 7.5 miles more if he walks at 9 mph. What was the total distance he covered?
Q. An executive rode from his home to an airport where a helicopter was waiting at an average speed of 30 mph. The executive boarded the helicopter and travelled at a pace of 60 miles per hour to the corporate headquarters. The total distance travelled was 150 miles, and the journey took three hours. Calculate the gap between the airport and the corporate headquarters.
Q. A boat sails for three hours against a three-mph current before returning the same distance in four hours. In calm water, what is the boat’s speed?
Must Read: Data Interpretation Questions And Tricks To Solve Them
Thus, these were different types of time and distance questions. These questions become easier once you understand the right way to approach these questions.
Check out this video to get handy with some important Time and Distance Tricks:
Time and Distance Questions Worksheet
Now that we have practiced ample time and distance questions, it is now time to solve a worksheet on it.
Time, Distance and Speed Conversions
Quickly get these conversions handy as they may assist you in solving the time and distance questions-
- To convert from km / hour to m / sec, we multiply by 5 / 18. So, 1 km / hour = 5 / 18 m / sec
- To convert from m / sec to km / hour, we multiply by 18 / 5. So, 1 m / sec = 18 / 5 km / hour = 3.6 km / hour
- Similarly, 1 km/hr = 5/8 miles/hour
- 1 yard = 3 feet
- 1 kilometer= 1000 meters = 0.6214 mile
- 1 mile= 1.609 kilometer
- 1 hour= 60 minutes= 60*60 seconds= 3600 seconds
- 1 mile = 1760 yards
- 1 yard = 3 feet
- 1 mile = 5280 feet
- 1 mph = (1 x 1760) / (1 x 3600) = 22/45 yards/sec
- 1 mph = (1 x 5280) / (1 x 3600) = 22/15 ft/sec
- For a certain distance, if the ratio of speeds is a : b, then the ratio of times taken to cover the distance would be b : a and vice versa.
Must Read: Ratio and Proportion Problems
The formula is as follows:
Speed = distance/time. This implies that, Time = distance/speed and Distance = Speed x Time.
To convert km/h to m/s, we multiply by 5 / 18. So, 1 km / hour = 5 / 18 m / sec.
To convert miles to feet, we multiply the given value in miles with 5280 to obtain the value in feet.
We understand that each and every topic of the GMAT exam is important and continuous practice can get you to your desired score. The Leverage Edu experts can equip you with the essential GMAT preparation tips as well as teach you all the essential concepts to crack GMAT to get you into your dream college.