Time, Speed and Distance Tricks

• Speed = Distance/Time  
• Unit = kilometer/hour (km/hr.) or, meter/second (m/s). 
• 1km = 1000m. 1 hr. = 60 60 = 3600sec. 
• Conversion of km/hr. to m/s: - 1000m/3600 sec = 5/18 m/s. 
• Conversion of m/s to km/hr.: - 18/5 km/hr.

Concept 1:

Speed is always inversely proportional to time and vice-versa i.e. Speed ∝ 1/time (Keeping distance as Constant).
Ex: - Let distance is 80km, the speed of car ‘A’ is 4km/hr. and speed of car ‘B’ is 8km/hr.
Solution: Time taken by Car A = 80/4 = 20 hr. and Car B = 80/8 = 10hr.
So, Sa : Sb = 4 : 8 = 1:2
Ta : Tb = 20:10 = 2:1

Concept 2:

Speed is directly proportional to distance travelled and vice-versa i.e. Speed ∝ Distance (Keeping time as Constant).
Ex: - Let distance travelled by car A is 80km in 1hr. and distance travelled by car B is 40km in 1 hr.
Solution: Speed of Car A = 80/1 km/hr. = 80km/hr. and Car B = 40/1= 40km/hr.
So, Da : Db = 80 : 40 = 1: 2.
Sa : Sb = 80 : 40 = 1 : 2.

Concept 3:

Time is directly proportional to distance travelled and vice-versa i.e. Time ∝  Distance (Keeping speed as constant).
Ex: - Let distance travelled by car A is 80km at a speed of 4 km/hr. and distance travelled by car B is 40km at a speed of 10 km/hr.
Solution: Time taken by Car A = 80/4 = 20 hr. and Car B = 40/4 = 10 hr.
So, Da : Db = 80 : 40 = 2 : 1
Ta : Tb = 40 : 10 = 2 : 1

Questions:

Question 1: Walking at a speed 25% more than that of usual speed a person reaches his office 8 minutes earlier. Find the usual time required for reaching office.
Solution: We will solve this question by 2 methods:
Basic Concept: Let usual speed be ‘s’ and usual time was taken is ‘t’. Then new speed is ‘1.25s’ and new time taken is (t-8).
Note: In this question, the unit of any parameter is not required.
Since the distance is constant. We can apply the basic formula, distance = speed ✖ time.

➪i.e. S1 ✖ T1 = S2 ✖ T2.
➪ s ✖ t = 1.25s ✖ (t-8)
➪ 0.25t = 10
➪ t = 40 minutes.

Shortcut method:
By taking ratio of usual and new speed i.e. s:1.25s = 4:5

Now we can take the difference of new and usual time and that will be equal to 8 minutes.
➪ 5x – 4x = 8
➪ x = 8.
So usual time taken = 8x = 40 minutes.
We will see some more questions in the next Article.