# Time and Distance - Aptitude test, questions, shortcuts, solved example videos

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## Time and Distance

Time & Distance is one of the most important chapters for any entrance exam. The concepts of this chapter help you in dealing effectively with the other two chapters i.e “Trains” and “Boats & Streams”.

Important Points to Remember

1) Speed is defined as the distance travelled per unit time.
 Speed = Distance Time

2) If same distance X is travelled at two different speeds S1 & S2, then average speed is calculated by,
 Average Speed (Sa) = (2S1S2) (S1 + S2)

3) Two bodies A and B move between two points P & Q. One starts from P and goes to Q while the other starts from Q and goes to P. They meet on the way and reach their destinations in time ta and tb respectively after meeting . Their speeds Sa & Sb are given by,

 Sa = tb Sb ta

4) When two bodies move in opposite direction, their speeds are added to find the relative speed.

SR = S1 + S2

5) When two bodies move in same direction, their speeds are subtracted to find the relative speed.

SR = S1 – S2

Conversion of Units

It is extremely important to pay attention to the units for each of the quantities given. At times, you may be required to convert the unit of speed from km per hr to metre per second or vice versa.

Converting km/hr into m/s

 km = 1000 m = 5 m/s hr 60 x 60 sec 18

Example:
 20 km = 20 x 5 = 5.55 m/sec hr 18

Converting m/s into km/hr:

 m = 18 km/hr s 5

Example:
 20 m = 20 x 18 = 72 km/hr s 5

- To convert minutes into seconds, multiply by 60
- To convert hours into seconds, multiply by 60 x 60

Question Variety

Basically there are 4 types of questions that are asked from this chapter. Understanding and practicing each of the 4 types will help you deal successfully with the problems from this chapter.

Type 1: Calculate either time, speed or distance from the other two given parameters.

Examples:

Q 1. How many seconds does Puja take to cover a distance of 500 m, if she runs at a speed of 30 km/hr?

a) 60 sec
b) 82 sec
c) 95 sec
d) 100 sec
View solution

Hint:

 Time = Distance Speed
We see that the distance is given in metres while the speed is given in km/hr and the answer is asked in seconds.
 So, convert km/hr into m/s by multiplying 5 m/s to the given value of speed. 18

 30 km = 30 x 5 = 75 m/sec hr 18 9
i.e. Place these values in the formula:
 Time = 500 x 9 = 60 sec 75

Q 2. A cyclist covers a distance of 800 meter in 4 minutes 20 seconds. What is the speed in km/hr of the cyclist?

a) 6.2 km/h
b) 8.4 km/hr
c) 11.05 km/hr
d) 16.07 km/hr
View solution

 Speed = Distance Time
Hint: Convert minutes into seconds
Time=4 min 20 sec =260 sec
 Speed = 800 = 3.07 m/sec 260

Convert the speed from m/s to km/hr by multiplying with (5/18)
 3.07 x 18 km/hr = 11.05 km/hr 5

Q 3. A man walking at the rate of 6 km/hr crosses a bridge in 15 minutes. The length of the bridge is ______.

a. 1000 m
b. 1250 m
c. 1500 m
d. 1800 m
View solution

Hint: To find the answer in meter, we will first convert distance from km/hour to meter/sec by multiplying it with 5/18 .Also, change 15 minutes to seconds by multiplying it with 60.

Distance = Speed x Time

1. Convert speed into m/sec:

 6 x 5 m/s = 1.66 m/s 18

2. Convert time from minutes into seconds = 15 x 60 s = 900 sec

3. Calculate : Distance = 1.66 x 900 = 1500 m

Type 2: Calculate speed of two people moving between two points, A and B, in opposite directions & crossing each other on the way.

Examples:

Q 4. Two girls move in opposite directions, one from A to B and other from B to A. The girl from A reaches the destination in 16 hrs and girl from B reaches her destination in 25 hrs, after having met. If former's speed is 25 km/hr, what will be the speed of latter?

a) 10 km/hr
b) 12 km/hr
c) 16 km/hr
d) 20 km/hr
View solution

Hint: If two bodies A and B move from each other's starting point in opposite directions, they reach their destinations after having met, then their speeds Sa & Sb are given by,

 Sa = tb Sb ta

where t is the time taken by them to cover the distance.
 Sb (25 x 4) = 20 km/hr 5

Q 5. Two buses start at the same time, one from P to Q and the other from Q to P. If both buses reach after 4 hours and 16 hours at Q and P respectively after they cross each other, what would be the ratio of speeds of the bus starting from P and that of the one starting from point Q?

a. 2 : 1
b. 1 : 2
c. 2 : 2
d. 1 : 4
View solution

Correct Option: (a)

Hint:

 SP = tQ SQ tP

SP and SQ are speeds of two the buses at points P and Q respectively.
tP = 18 hrs and tQ = 4 hrs
 SP = 16 SQ 4

 Therefore, ratio of speeds Sp = 4 = 2 SQ 2 1

One bus travels at a speed twice of the other bus.

Type 3: Finding Relative Speed for two bodies moving in same or opposite directions.

Examples:

Q 6. Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other?

a. 2.45 p.m.
b. 2.30 p.m.
c. 1.35 p.m.
d. 1.15 p.m.
View solution

Hint: We have read, relative speed between two bodies moving in opposite direction: SR = S1 + S2

Assume, distance traveled by P in x hrs = 25 x km -----(1)
distance traveled by Q in (x-1) hrs = 20 (x-1) km -----(2)

25 x + 20 (x -1) = 275

x = 6.5 hrs

(x -1) = (6.5 -1) = 5.5 hrs

Time at which they cross each other = 9 a.m. + 5.5hrs = 2.30 p.m.

The two motorcycle riders cross each other at 2.30 p.m.

Type 4: Numericals on Average Speed when the same part of total distance is traveled at two or more different speeds.

Examples:

Q 7. An aeroplane flying 1000 km covers the first 200 km at the rate of 200 km/hr, the second 200 km at 400 km/hr, the third 200 km at 600 km / hr & last 200 km at the rate of 800 km/hr. Determine the average speed of the aeroplane.

a. 250 km/hr
b. 300 km/hr
c. 480 km/hr
d. 600 km/hr
View solution

Hint: We know that,

 Time = Distance Speed

 Total time taken = 200 + 200 + 200 + 200 = 25 200 400 600 800 12

 Average speed = 1000 x 12 = 480 km/hr 25

Q 8. Jennifer travels first 4 hours of her journey at a speed of 80 miles/hr and the remaining distance in 6 hours at a speed of 30 miles/hr. What is her average speed in miles/hr?

a. 50 miles / hr
b. 60 miles / hr
c. 75 miles / hr
d. 92 miles / hr
View solution

Hint : If time and speed are given then the average speed is calculated by considering the total distance covered and the total time required.

i.e. Average speed = Total distance / Time

Distance =Time x Speed

Total distance covered by Jennifer = Distance covered in first 4 hours + distance covered in next 6 hours

= (80 x 4) + (30 x 6)

= 500 miles / hr

Total time taken to complete the journey = 4 + 6 = 10 hrs

Therefore,

 Average Speed = Total Distance Time

= 500 / 10

= 50 miles/hr

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