Time, Speed & Distance

I. Basics of Speed:

                             SPEED = DISTANCE / TIME

Speed & Distance are directly proportional when time is constant. 

Speed & Time are inversely proportional when distance is constant.

Important Conversions :-

1 kmph = 5/18 meter/second (mps)

1 mps = 18/5 kmph

1 mile = 1.6 km (approx)

If the speed of object changes in ratio of x:y then

time taken changes in ratio of y:x when distance to cover is same

& distance covered changes in ration of x:y when time taken is same.

Q1. A man is traveling at speed of 15kmph to cover distance of x km. On return journey he travels at 10kmph. What is ratio of time taken to cover distance to return journey ?
(1) 3:2 (2) 2:3 (3) 4:5 (4) 1:1 (5) 3:4


Solution:- Complexity - Easy

If the speed of object changes in ratio of 15:10 then

time taken changes in ratio of 10:15 when distance to cover is same.
i.e. 2:3 Hence answer option 2.


II. Average Speed :-

average speed is one of the most important concept of speed ,distance & time.


average speed =  total distance / total time. 


type 1:- different speeds & different distances
Q2. A man covers the first 150 km of his journey from Mumbai to Pune at speed of 50 kmph, then next 120 km at a speed of 40 kmhr & remaining 180 km at a speed of 60 kmhr. What is average speed of the entire journey ?
(1) 42 kmph (2) 50 kmph (3) 52 kmph (4) 56 kmph (5) 57.5 kmph


Solution:-

average speed =  total distance / total time. 

total distance = 150 + 120 + 180 = 450 km

total time = 150/50 + 120/40 + 180/60 = 3 + 3 + 3 = 9 hrs.

average speed = 450 / 9 = 50 kmph. Hence answer option 2.

type 2:- constant distance

Q3. A person cover covers three equal distances of race track at speed of 20kmph, 30kmph & 40 kmph. What is average speed ?

(1) 25.70 kmph (2) 27.70 kmph (3) 30 kmph (4) 32.70 kmph (5) 37.70 kmph

Solution:-

let the distance of one stretch be D.

Total Distance = 3D

Total Time = D/20 + D/30 + D/40

Average Speed =  3D / (D/20 + D/30 + D/40) = 27.69 kmph. Hence answer option 2.

type 3:- constant time

Q4. A person travels at a particular journey at three different speeds : 40kmph, 60 kmph & 80 kmph each for equal intervals of time. What is his average speed ?

(1) 50 kmph (2) 55.70 kmph (3) 60 kmph (4) 65.70 kmph (5) 70.00 kmph

Solution:-  when time is constant, average speed is arithmetic mean of speeds. Hence answer is option 3.

type 4:- different time & different speeds.

Q5. Rahul travels his first 2 hours of journey at speed of 25 kmph, next 3 hours at 30 kmph & remaining 4 hours at speed of 35 kmph. What is his average speed of entire journey ?

(1) 28.33 kmph (2) 30.00 kmph (3) 31.11 kmph (4) 33.33 kmph (5) 34.33 kmph

Solution:-

Total distance = 2*25 + 3*30 + 4*35 = 50 + 90 + 140 = 280 km

Total Time = 2 + 3 + 4 = 9 hours

Average Speed = 280 / 9 = 31.11 kmph. Hence answer option 3.
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Time taken after meeting (same distance):-

if 2 persons starts journey from A & B and move towards each other and meet at C, after meeting they reach opposite points in x & y hrs respectively.

then speed before they meet is  √y : √x

Q6. Seeta start her journey from Mumbai towards Pune at speed of  20 kmph & her sister Geeta starts her journey from Pune towards Mumbai at speed of 30 kmph. They meet at Lonavala. What is ratio of time taken by them to reach their destinations after they meet ?

(1) 9:4 (2) 2:3 (3) 3:2 (4) 1:1 (5) Data insufficient

Solution :-

Speed before they meet is x:y i.e. 20:30

time after they meet will be y²:x² = 900 : 400 = 9:4. Hence answer option 1.

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III.Relative Speeds:-

when two objects are moving in the same direction : related speed is difference of their speeds.
when two objects are moving in opposite directions : related speed is sum of their speeds.


Q7. Policeman is chasing a Gangster. Policeman is at speed of 20kmph & Gangster is at speed of 15 kmph. Distance between them is 25 kms. How much time will Policeman take to catch Gangster?
(1) 1 hours (2) 2.5 hours (3) 3 hours (4) 3.33 hours (5) 5 hours

Solution:-
Distance to cover = 25 kmph
Relative speeds of objects = 20 - 15 = 5 kmph ( as they are moving in same direction)
Time taken = 25 / 5 = 5 hours. Hence answer option 5.


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