Definition, Formulas, and Questions and answers of Speed , Time and Distance !

TIME SPEED AND DISTANCE

Speed, Time & Distance Conversions

• 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 kilometer1 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.

How to Calculate Average Speed ?

           Often calculating the average speed is simple using the formula

                           

                                Speed=Distance/Time

However, you may be given two alternative speeds to utilise for separate periods of time or across various distances. Other formulae for calculating the average speed exist in these cases. These sorts of issues may be useful in real life, and they frequently arise on standardised examinations, so learning these formulae and procedures is beneficial.

 

Relationship Between Speed, Time & Distance

•  Distance/Time = Speed — This shows us how fast or slow an item moves. It is defined as the distance travelled divided by the time it took to travel that distance.
•  Distance is directly proportional to speed, but time is inversely proportionate. As a result, Distance = Speed X Time, and Time = Distance / Speed, the time taken will reduce as the speed rises, and vice versa.
•  Any simple problem may be addressed using these formulae. However, while utilising formulae, it's also crucial to remember to use the right units.
   

Speed, Time, and Distance Tricks

Now, we come across time speed and distance on a daily basis, but we don't really think about the relationship until we put it to the test. If you drive to work at 4 km/hr, you will arrive 20 minutes late; if you drive at 6 km/hr, you will arrive 10 minutes early. Isn't that easy? Competitive tests, on the other hand, manage to perplex us by translating kilogrammes to metres or centimetres, and hours to seconds and milliseconds.
 

QUESTIONS AND ANSWERS:

Question 1: 

A moving train crosses a man standing on a platform and a bridge 300 meters long in 10 seconds and 25 seconds respectively. What will be the time taken by the train to cross a platform 200 metres long?

 

Option 1: 25sec

Option 2: 22sec

Option 3: 20sec

Option 4: 28 sec

Answer: 3: 20sec

Question 2: 

The ratio of length of two trains is 5:3 and the ratio of their speeds is 6:5 . The ratio of time taken by them to cross a pole is? 

Option 1: 25 : 18 

Option 2: 23:18

Option 3: 18:25 

Option 4: 25:17

Answer: 1:  25 : 18 

Question 3:

 A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is?

Option 1: 180mm

Option 2: 200mm

Option 3: 120mm

Option 4: 250mm  

Answer: 2:  200m 

Explanation: In both cases, the speed of the train is constant, and then we have 100/60=(x+800)/(x+400) 100(x+400)=60(x+800) x=200m
 

Question 4: 

The length of a train and that of a platform are equal. If with a speed of 90 km/hr the train crosses the platform in one minute.?  

Option 1:720 mm 

Option 2:700mm

Option 3:750mm

Option 4:780mm

Answer: 3: 750m

Explanation: Let length of both train and platform = x. Distance covered by the train to cross the platform = x + x = 2x Time = 1 min = 60 sec and speed = 90 km/h 90×5/18=25m/s Therefore, Distane = Speed×Time 2x = 25 x 60 x = 750 m 
 

Question 5: 

Gautama covers a distance of 160 km at a speed of 32 km / h and then returns at a speed of 40 km / h. What is the average speed of Gautam?

Option 1: 72 km/h 

Option 2: 71.11 km/h

Option 3: 36 km/h 

Option 4: 35.55 km/h

Answer: 4: 35.55 km/h

Explanation: Total time taken in complete travelling = 160/32+160/40= 9 hour So, The average speed of Gautam = 160 + 160 9 = 35. 55 km/h.

Question 6: 

A farmer travelled a distance of 61 km in 9 hrs. He travelled party on foot at the rate of 4 km/hr and party on bicycle at the rate of 9 km/hr. The distance travelled on foot is—  

Option 1: 17 km

Option 2: 16 km

Option 3: 15 km

Option 4: 14 km

Answer: 2: 16 km

Question 7: 

Walking at the rate of 4 kmph a man covers certain distance in 2 hrs 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in how many minutes ? 

Option 1: 35 min 

Option 2: 40  min 

Option 3: 45 min 

Option 4: 50 min 

No answer is set

Explanation: When distance is constant, then speed is inversely proportional

Question 8:

Two trains of lengths 150 m and 180 m respectively are running in opposite directions on parallel tracks. If their speeds be 50 km/hr and 58 km/hr respectively, in what time will they cross each other ?

Option 1: 30 sec.

Option 2: 15 sec.

Option 3: 22 sec.

Option 4: 11 sec.

Answer: 4: 11 sec

Question 9: 

Two trains start at the same time from Aligarh and Delhi and proceed towards each other at the rate of 14 km and 21 km per hour respectively.  When they meet, it is found that one train has travelled 70 km more than the other. The distance between two stations is 

Option 1: 350 km 

Option 2: 140 km

Option 3: 210 km

Option 4: 300 km

Answer: 1: 350 km   

Explanation: Difference in speeds = 14 – 21 = 7 km/h. Time taken in journey 

(Till meating) = 70 /10= 7 hrs. Total distance of between both stations

 = 10 (14 + 21) = 350 km.
 

Question 10:

A car travels at a speed of 60 km/h and covers a particular distance in 1 h. How long will it take for another car to cover the same distance at 40 km/h ?   

Option 1: 3/2 h 

Option 2: 1 h 

Option 3: 5/2 h

Option 4: 2 h 

Answer: 1: 3/2 h   

Explanation:

 

Question 11:

Two men start together to walk a certain distance, one at 4 km/h and another at 3 km/h. The former arrives half an hour before the latter. Find the distance.

Option 1: 6 km

Option 2: 9 km

Option 3: 8 km

Option 4: 7 km

Answer: 1: 6 km

Explanation: Let the distance = x km According to question, 

x/3 - x/4 = 1/2 * 4x - 3x/12 = 1/2 x 12 = 1/2 x = 6 km
 

Question 12:

The speed of a bus is 72 km/h. The distance covered by the bus in 5 second  is

Option 1: 50 m 

Option 2: 74.5 m

Option 3: 100 m

Option 4: 60 m

Answer: 3: 100 m

Question 13: 

Mohan covers a distance of 2.5 km by scooter at the rate of 30 km/h. The time taken by Mohan to cover the given distance in minutes is

Option 2: 6 

Option 3: 8 

Option 4: 5

Answer: 4: 5 

Explanation: Given, distance travelled = 2.5km 

Speed= 30km/h

Then, time taken = distance/speed= 2.5/30= 1/12

= 60/12= 5 min 
 

Question 14:

Given that the lengths of the paths of a ball thrown with different speeds by two guys are the same, and that the average speed for the first and second throws are respectively 90km/h and 162 km/h, then what is the time taken by the first throw to cover the length if the same for the second thrown is one second ?

Option 1: 3/2 sec

Option 2: 1 sec

Option 3: 2/3 sec

Option 4: 9/5 sec

Answer: 4:  9/5 sec

For same length

S1 × T1 = S2 × T2 

90 × 5/18 ×T1 = 162 × 5/18×1 

multiplied by 5/18 to convert in m/sec 

25 × T1 = 45 

T1 = 45/25=9/5 sec
 

Question 15:

A passenger train takes 1 hr less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed, what is its usual speed?

Option 1: 40 km/h 

Option 2: 25 km/h 

Option 3: 30 km/h 

Option 4: 36 km/h 

Explanation: 

⇒ Let the usual speed of the train be x km/hr

⇒ Distance covered in the journey=150km 

⇒ Time taken by the train with usual speed =150/x hr

⇒ New speed of train =(x+5)km/hr

⇒ Time taken by the train after increasing the speed =150/ (x+5) hr            ⇒(150/x)−150/(x+5) =1 

⇒ 150(1/x−1/(x+5))=1 

⇒ 150(5)=x(x+5) 

⇒ 750=x 2+5x 

⇒ x 2+5x−750=0 

⇒ x 2+30x−25x−750=0 

⇒ x(x+30)−25(x+30)=0 

⇒ (x+30)(x−25)=0 

⇒ x+30=0 and x−25=0 

⇒ x=−30 and x=25 ∴ The usual speed of the train = 25km/hr 
 

Question 16:

Two places P and Q are 162 km apart. A train leaves from P to Q and at the same time another train leaves from Q to P. Both the trains meet after 6 hours. If the train travelling from P to Q travels 8 km/hr faster than the other train, find the speed of both the trains?

Option 1:  9*1/2  and 17*1/2

Option 2:  9*1/2 and 19*1/2

Option 3:  7*1/2 and 17*1/2

Option 4:  none of these  

Answer:  1:  9*1/2  and 17*½ 

Explanation:

then , speed of first train = 9*1/2 km/h 

and speed of second train = x+8 = 9 *1/2 +8 = 17 1 2 km/h

Question 17:  

If a man covers a distance between his house and office on scooter having an average speed of 30 km/hr. he gets late by 10 min. However if he covers with a speed of 40 km/hr. he reaches his office 5 min earlier. What is the distance between his house and office?

Option 1: 36

Option 2: 30 

Option 3: 40

Option 4: 42

Answer: 2: 30

Explanation: When speed is 30 km/hr he reaches 10 minutes late when Speed is 40 km/hr he reaches 5 minutes earlier. 

Let Distance =D  so, D/30−D/40 =15min (4D-3D)/120 = 15/60 then,D=30 km.
 

Question 18:

A boy walks at a speed of 10 km/hr. and reaches his school 15 min late. If he increases his speed by 2 km/hr. he gets late by 5 minutes. Find the distance between his school and house?

Option 1: 15

Option 2: 12

Option 3: 10

Option 4: 16 

Answer: 3: 10

Explanation:

let the distance of school from house = x and time = t

speed of boy = 10 km/hr

he is late by = 15 mins = 15/60 hr

=> x/10 = t - 15/60 => (x/10) + (15/60) = t. - - - (1)

then ,speed increased by = 2 km/hr 

new speed = 10 + 2 = 12km/hr

he is late by = 5 mins = 5/60 hr 

=> x/12 = t - (5/60) 

=> (x/12) + (5/60) = t. - - -(2) equating (1) and (2) 

x/12. + 5/60. = x/10 + 15/60 => x/12 - x/10. 

= (15-5)/60 => x/60 = 10/60 => x = 10 km

Question 19:

Excluding stoppage the speed of bus is 54 km/ hr including stoppage it is 45km/hr. How many minutes does the bus stops per hour? 

Option 2: 15 min

Option 3: 10 min

Option 4: 18 min

Answer: 3: 10 min

 =  9 × 60/54   = 10 minutes
 

Question 20:

The speed of two trains are in the ratio of 7: 9. They are moving in the opposite direction on parallel track. The first train crosses a telegraph pole in 4 seconds whereas the second train crosses the pole in 6 seconds. Find the time taken by trains to cross each other?

Option 1: 36sec

Option 2: 43sec

Option 3: 39sec

Option 4: 41sec

Answer: 4: 41sec

let s1=7x and s2 =9x 

now length of first train is a 

and length of second train is b. 

first train cross pole in 4sec,; 4=a/7x 

a=28x 

second train cross pole in 6sec; 6=b/9x 

b=54x 

now required time =(a+b)/s2-s1= (54x+28x)/9x-7x=82x/2x

=41sec

 

 

What is the Relationship Between Speed, Time & Distance ?

•  Distance/Time = Speed — This shows us how fast or slow an item moves. It is defined as the distance travelled divided by the time it took to travel that distance.

•  Distance is directly proportional to speed, but time is inversely proportionate. As a result, Distance = Speed X Time, and Time = Distance / Speed, the time taken will reduce as the speed rises, and vice versa.

•  Any simple problem may be addressed using these formulae. However, while utilising formulae, it's also crucial to remember to use the right units.

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