Time, Speed & Distance

Time, Speed & Distance

Important Formula

Units conversion

(1) units of Distance are km and m.

(2) Time is measured in hour, minute and seconds.

(3) Unit of speed : km/hour and m/sec.

Some important questions-

Q.1 A person travels a distance of 56km in 3 hour 30 minutes. Calculate his speed.

Solution- time taken= 3 hr 30 min= 3.50 hr

Q.2 A train is running at a speed of 25km/hr. how much distance will it cover in 3 hour 30 minutes.?

Solution-

Q.3 A bus travelled 15000 metres of 54km/hr. Find out the time taken by the bus in the whole journey (in speed)

Sol- 

Relative speed

1 if two bodies with speeds of ‘x’ km/hr and ‘y’ km/hr respectively are moving in the same direction then their relative speed.

Will be (x-y) km/hr [where x>y]

2 If two bodies with speeds of ‘x’ km/hr and ‘y’ km/hr respectively are moving in opposite directions then their speed will be (x+y) km/hr.

Important questions-

Q .1 Two trains are running towards each other at the speed of 50kmph and 40 kmph. Find out their relative speed in metre/ second.

Sol : Relative speed= 50+40=90kmph


Q.2 Two trains are running in the same direction at speed of 140kmph and 68 kmph. Find out relative speed in m/s.


Ratio theorem :

If the speed of the body changes from a : b (a to b), then the time taken to cover the same distance will change by b : a (b to a)


i.e. Speed is inversely proportional to time ; means if speed increases then time decrease and if speed decrease then time increases.

If two bodies are running at the speed ratio of x : y, then time taken to cover the same distance will be in the ratio of y : x


Important questions-

Q.1 Three trains are running at a speed ratio of 4 : 5 : 6. Find out ratio of time taken by them to cover a certain distance.

Sol-


Q .2 A train takes 50 minutes to cover a distance at a average of 48kmph. Find the speed at which the train must run to reduce the time of journey to 40 minutes.

Sol:- Ratio of time taken= 50 : 40 =5 : 4

Ratio of speed= 4 : 5

If 4x=48,  then x= 12


Q.3 If ‘A’ travels of his usual speed, he takes 20 minutes more than actual time. Find out the actual time of journey.

Ratio of time taken= 5 : 3

Difference= 2 units= 20 minutes

1 unit= 10 minutes

Average speed

If half of the distance is covered at a speed of ‘x’ kmph and the remaining half distance at a speed of ‘y’ kmph, then average speed during the journey.


Q.1 A man goes to his office from home at a speed of 30kmph and comes back to his home by motorcycle at a speed of 70kmph. Find out his average speed.

Sol- 

2 Rohit went to Delhi from Jaipur at a speed of 40kmph and returned to Jaipur at a speed of 60kmph. If the whole journey took 5 hours, then what is the distance between Jaipur and Delhi?

Sol-

          

3 A person walks 10 km at a speed of 5kmph. Then he travels at a speed of 20kmph and completes the remaining distance of 60km journey by bike at a speed of 40kmph. Find out his average speed during the whole journey.

 

Theorem I :

If a person travels certain distance at a speed of x kmph, he reaches late by minutes, and if he travels the same distances at a speed of Y kmph, then he reaches minutes earlier than the original time.

Then distance travelled

Q. If sanjay walks at a speed of 10kmph, he reaches his school 20 minutes late and if he walks at a speed of 12kmph, then he reaches 10minutes earlier than the original time. How much is the distance of his school?

Sol-

Theorem 2:

If two persons A and B start from two points P and Q respectively in opposite directions towards each other and after passing each other, they complete the journey in ‘a’ and ‘b’ hour respectively, then ratio of their.

Q. two buses start at the same time from Jaipur and Udaipur. After meeting each other, they take 4 hr and 9 hr respectively. to reach Udaipur and Jaipur. Find the ratio of the buses.

 

Theorem 3 :

 If two vehicles start from points P and Q respectively at a respective speed of ‘x’ and ‘y’ kmph in same or opposite direction, then time taken by them to meet each other.


Q A plane takes off from an airport at 9 .00 a.m. at a speed of 600kmph and another plane takes off from the same airport at 9.30 a.m. at a speed of 700kmph in the same direction. At what time will B cross A ?


Q. A and B start from Point P and Q respectively at a speed of 30kmph and 42kmph towards each other at 12.00 noon. if they meet each other at 3 : 30 p.m. then what is the distance between P and Q?


Stoppage question theorem :

A train’s average speed is ‘x’ kmph without any stoppage. With stoppages, its average speed becomes ‘y’ kmph, then


Q. Average speed of a train without stoppages is 54kmph and its average speed with stoppages is 45kmph. Find out the stoppage time per hour.

Sol-