Speed, Time and Distance

Speed, Time, and Distance is a fundamental concept in mathematics that deals with the relationship between the speed of an object, the time it travels, and the distance it covers.

Basic Concepts

1. Speed: The rate at which an object moves, typically measured in units of distance per unit time (e.g., km/h, m/s).

Formula: Speed = Distance/Time

2. Time: The duration for which an object travels, typically measured in units of time (e.g., hours, minutes, seconds).

Formula: Time = Distance/Speed

3. Distance: The length of the path traveled by an object, typically measured in units of distance (e.g., kilometers, meters).

Formula: Distance = Speed × Time

Unit Conversions

• 1 km/hr = 5/18 m/sec

• 1 m/sec =  18/5 km/hr

Types of Problems:

A. Basic Speed Problems

Example: Q. A man covers 120 km in 3 hours. Find his speed.

Solution: Speed = 120 ÷ 3 = 40 km/hr

B. Relative Speed Used when two objects are moving toward or away from each other.

Same direction: Relative speed = |S1 - S2|

Opposite direction: Relative speed = S1 + S2

Example: Q. Two trains of speeds 50 km/hr and 70 km/hr move in opposite directions. How fast are they moving relative to each other?

Solution: 50 + 70 = 120 km/hr

C. Train Problems

Train crosses a pole: Time = Length of the train/Speed

Train crosses a platform: Time = (Length of the train + platform)/Speed 

Example: Q. A train 300 m long crosses a platform 200 m long in 30 seconds. Find speed.

Solution: Speed = (300 + 200)/30

= 500/30

= 16.67 m/s

= 16.67 × 18/5

= 60 km/hr 

D. Average Speed

For equal distance:

Average Speed = 2xy/x + y 

Example: Q. A car goes to a place at 60 km/hr and returns at 40 km/hr. What is the average speed?

Solution: Average Speed = (2×60×40)/60+40

= 4800/100

= 48 km/hr