Time, Speed & Distance: Formulas, Solved Quantitative Aptitude MCQs

Understanding the relationship between time, speed, and distance is essential in solving quantitative aptitude questions. Whether calculating the time taken for a journey, the speed of a moving object, or finding the distance covered, these concepts are fundamental in aptitude tests.

Relationship Between Time, Speed And Distance

When an object moves at a certain speed for a specific amount of time, it covers a certain distance. This can be expressed using the formula:

Distance= SpeedxTime.

Conversely, if you know the distance and speed, you can calculate the time taken by rearranging the formula:

Time= Distance/Speed.

Likewise, the formula for speed is Speed= Distance/Time.

Speed Impact On Time

When speed increases, the time required to cover a specific distance decreases. For instance, if a car travels at 60 miles per hour instead of 30 miles per hour, it takes half the time to reach a destination 60 miles away.

Average Speed Concept

Dividing the total distance travelled by the total time taken gives us the average speed. It provides a more realistic representation of an object's overall speed during a journey.

Click here to enhance and upskill your quantitative aptitude in time, speed and distance right away!

Conversion Units Time, Speed And Distance

The most common units for measuring speed include meters per second (m/s), kilometres per hour (km/h), and miles per hour (mph). Time can be measured using different units such as seconds, minutes, and hours. Here are the common conversion units for time, speed, and distance:

Conversion	From	To	Value
Speed Conversions
1 km/h	kilometres per hour (km/h)	meters per second (m/s)	0.277 m/s
1 m/s	meters per second (m/s)	kilometres per hour (km/h)	3.6 km/h
1 mph	miles per hour (mph)	kilometres per hour (km/h)	1.609 km/h
1 knot	knots	kilometres per hour (km/h)	1.852 km/h

Time Conversions
1 hour	hours	minutes	60 minutes
1 hour	hours	seconds	3600 seconds
1 minute	minutes	seconds	60 seconds

Distance Conversions
1 kilometer	kilometres (km)	meters (m)	1000 meters
1 mile	miles	kilometres (km)	1.609 km
1 meter	meters (m)	centimetres (cm)	100 centimetres
1 foot	feet	meters (m)	0.3048 meters

Average & Relative Speed: Two Trains Moving in the same or opposite direction

Average speed	Average speed= Total distance travelled/Total time taken
Average speed (When distance is constant)	2xy/x+y
Relative speed (If two trains are moving in opposite directions)	Relative speed=X+Y Time taken= L₁+ L₂/X+Y Where L₁ & L₂are the lengths of the two trains
Relative speed (If two trains are moving in the same direction)	Relative speed=X-Y Time taken= L₁+ L₂/X-Y Here, L₁ & L₂are the lengths of the trains

Solved MCQs on Time, Speed And Distance

Time, speed and distance concepts are commonly tested in quantitative aptitude exams through various question types:

Question 1. Jayshree goes to the office at a speed of 6 km/h and returns to her home at 4 km/h. If she takes 10 hours, what is the distance between her office and home?

(a) 24 km

(b) 12 km

(d) 30 km

Solution: a) 24 km

Explanation: Solve using the options

d/6 + d/4 = 10

Using the option a) 24

24/6 + 24/4 = 10

4 + 6 = 10

10 = 10

So, the correct option is a)24 km.

Question 2. A and B travel the same distance at the rate of 8 kilometres and 10 kilometres an hour, respectively. If A takes 30 minutes longer than B, the distance travelled by B is

(a) 6 km

(b) 10 km

(d) 20 km

Solution: d) 20 km

Explanation: Solve using options.

The value in option (d) fits the situation as

= d/8 – d/10

= 20/8 – 20/10 = 2.5 – 2 = 0.5 hours = 30 minutes.

Question 3. Ram and Shyam run a race of 200m. First, Ram gives Shyam a start of 200m and beats him by 30s. Next, Ram gives Shyam a start of 3 min and is beaten by 1000 metres. Find the time in minutes when Ram and Shyam can run the race separately.

(a) 8, 10

(b) 4, 5

(d) 6, 9

Solution: a) 4,5

Explanation: When Ram runs 2000 m, Shyam runs (1800 – 30s)

When Ram runs 1000 m, Shyam runs (2000 – 180s)

Then, 2000/1000 = 1800-30s2000-180s

Solving, we get s = 6.66 m/s.

Thus, Shyam’s speed = 400 m/minute, and he would take 5 minutes to cover the distance.

Question 4. A train requires 7 seconds to pass a pole, while it requires 25 seconds to cross a stationary train, which is 378 metres long. Find the speed of the train.

(a) 75.6 km/h

(b) 75.4 km/h

(d) 21 km/h

Solution: a) 75.6 km/h

Explanation: 7 x St = Lt

25 x St = Lt + 378

Solving, St = 21 m/sec = 21 X 18/5 = 75.6 kmph

Question 5. A boat sails down the river for 10 km and then up the river for 6 km. The speed of the river flow is 1 km/h. What should be the minimum speed of the boat for the trip to take a maximum of 4 hours?

(a) 2 km/h

(b) 3 km/h

(d) 5 km/h

Solution: c) 4 kmph

Explanation: Solve through options. For option (c) at 4 km/h, the boat would take exactly 4 hours to cover the distance.

d/10+d/6=1

4/10+4/6=1

Question 6. A boat sails 40 km upstream in 8 h and a distance of 49 km downstream in 7 h. The speed of the boat in still water is

(a) 5 km/h

(b) 5.5 km/h

(d) 6.5 km/h

Solution: c) 6km/h

Explanation: Upstream speed = 40/8 = 5 kmph.

Downstream speed = 49/7 = 7 kmph.

Speed in still water = average of upstream and downstream speed = 6 km/h.

Question 7. Vinay runs 100 metres in 20 seconds, and Ajay runs the same distance in 25 seconds. By what distance will Vinay beat Ajay in a hundred-metre race?

(a) 10 m

(b) 20 m

(d) 12 m

Solution: b) 20 m

Explanation: Speed of Vinay = 5 m/s; Speed of Ajay = 4m/s.

In a hundred-meter race, Vinay would take 20 seconds to complete, and this time, Ajay would only cover 80 meters. Thus, Vinay beats Ajay by 20 meters in a hundred-meter race.

Question 8. Vinay and Shyam participated in a 500-meter race where Vinay had a head start of 140 meters. The ratio of their speeds was 3:4. How much did Vinay win in the race?

(a)15 m

(b) 20 m

(d) 30 m

Solution: b) 20 m

Explanation: When Shyam does 500, Vinay does 375. Since Vinay has a start of 140 m, it means that Vinay only needs to cover 360 m to reach the destination.

When Vinay does 360, Shyam would cover 480 m and lose by 20 m. (Since the ratio of their speeds is 3:4)

Question 9. How many seconds will a caravan 120 metres long running at the rate of 10 m/s take to pass a standing boy?

(a) 10 s

(b) 12 s

(d) 14 s

Solution: b) 12 s

Explanation: Distance to be covered = 120 meters.

Speed = 10m/s; time required = 120/10 =12 seconds.

Question 10. The two trains departing from Muzaffarpur at different times, one at 8:30 a.m. and the other at 9:00 a.m., are travelling at speeds of 60 km/h and 70 km/h. How far from Muzaffarpur will the two trains meet each other?

(a) 210 km

(b) 180 km

(d) 120 km

Solution: a) 210 km

Explanation: When the second train leaves Muzaffarpur, the first train will have already travelled 30 km. Now, after 9 AM, the relative speed of the two trains would be 10 km/h (i.e. the rate at which the faster train would catch the slower train).

Since the faster train has to catch up a relative distance of 30 km for the trains to meet, it would take 30/10 = 3 hours to catch up. Distance from Muzaffarpur = 70 X 3 = 210 km.

Conclusion

Understanding the intricacies of time, speed, and distance is crucial for various real-life applications. The relationship between these elements is not only mathematical but also practical, influencing daily decisions and problem-solving scenarios. Individuals can enhance their quantitative aptitude skills and tackle speed-related problems with confidence by mastering the concepts discussed in this article.

To delve deeper into the realm of time, speed and distance calculations, readers are encouraged to practice solving a variety of problems across different contexts. Applying the strategies outlined here in diverse scenarios will not only solidify understanding but also sharpen analytical thinking. Embracing these principles will undoubtedly pave the way for improved problem-solving abilities in both academic and practical settings.

Frequently Asked Questions (FAQs)

1. How are time, speed and distance related in the context of physics?

In physics, speed measures how fast something moves. When an object goes faster, it takes less time to travel a certain distance.

2. What are some common units used to measure speed, time, and distance?

Speed is typically measured in units like meters per second (m/s) or kilometres per hour (km/h). Time can be measured in seconds, minutes, or hours. Distance is commonly measured in meters (m) or kilometres (km).

3. How can one convert between different speed, time, and distance units?

You can use conversion factors to convert units of speed, time, or distance. For example, to convert km/h to m/s, multiply by 5/18. Always ensure you understand the relationship between the units before converting.

4. How is average speed calculated when considering varying speeds during a journey?

To find the average speed, divide the total distance by the time taken. Make sure to consider any changes in speed by adding up the distances covered at each speed.

5. What role does inverse proportionality play in understanding speed concepts?

Inverse proportionality means that when one thing goes up, the other goes down constantly. For example, if time increases while distance stays the same, speed will decrease.

Kaihrii Thomas

Associate Content Writer

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