The terms time and distance are related to the speed of a moving object.
Speed: Speed is defined as the distance covered by an object in unit time.
Speed = Distance/Time
Some Important Facts:
* Distance travelled is proportional to the speed of the object if the time is kept constant.
* Distance travelled is proportional to the time taken if speed of object is kept constant.
* Speed is inversely proportional to the time taken if the distance covered is kept constant.
* If the ratio of two speeds for same distance is a:b then the ratio of time taken to cover the distance is b:a
i. If two objects are moving in same direction with speeds of x and y then their relative speed is (x - y)
ii. If two objects are moving in opposite direction with speeds of x and y then their relative speed is (x + y)
i. To convert 'X' Km/hr into m/s
- Multiply X with 5/18
ii. To convert 'x' m/s into Km/hr
- Multiply x with 18/5
Some Important Shortcut Formulas
If some distance is travelled at x km/hr and the same distance is travelled at y km/hr then the average speed during the whole journey is given by
Average speed = (2*x*y)/(x+y)
Ex: A peson travelled a distance with 8 km/hr and return the journey with 4 km/hr.then,the average speed during the journey ?
a. 5 km/hr b. 16/3 km/hr
c. 6 km/hr d. 12 km/hr
If a person travels a certain distance at x km/hr and returns at y km/hr, if the time taken to the whole journey is T hours then the one way distance is given by
Ex: If a person travels certain distance at 6 Km/hr and returns at 8 Km/hr, if the time taken to the whole journey in 7 hours.then,the one way distance ?
a. 16 b. 24 c. 8 d. 32
Sol: D= (7*8*6)/(8+6)= 24 km
If a car does a journey in ‘T’ hrs, the first half at ‘x’ km/hr and the second half at ‘y’ km/hr. The total distance covered by the car is :
(2 * Time * x * y )/ (x + y).
Ex: A motorcar does a journey in 10 hrs, the first half at 21 kmph and the second half at 24 kmph. Find the distance?
a. 124 b. 224 c. 225 d. 125
Sol: Distance = (2 x 10 x 21 x 24) / (21+24) = 10080 / 45 = 224 km.
If the same distance is covered at two different speeds S1 and S2 and the time taken to cover the distance are T1 and T2 ,then the distance is given by
D = [(s1*s2)/(s1-s2)]*(t2-t1)
Ex: A person travelled a distance with two different speeds 5 Km/hr and 6 km/hr and time taken to cover distance are 3 hrs and 4 hrs.the distance travelled by person ?
a. 30 km b. 20 km c. 15 km d. 38 km
Sol: D= [(5*6)/(5-6)]*(4-3) =30km
A distance covers in some time with S1 speed.if it takes T hr more to cover same distance with S2 speed. So, the distance is
D = (T*S1*S2)/(S1-S2)
Ex: A person covers a distance with 5 km/hr in some time.if he moves with 3 km/hr speed he covers the distance in 2 hr more.the distance travelled by person ?
a. 10 km b. 15 km c. 18 km d. 21 km
Sol: D= (2*5*3)/(5-3) = 15 km
If a distance traveled with S1.then,it takes T hrs late.same distance traveled with S2.then, it takes T hrs earlier.so,the distance is
D = (2*S1*S2*T)/(S2-S1)
Ex: A person travelled a distance with 5 km/hr then, he will take 2 hrs more.if he travels with 7.5 km/hr then,he will reach 2 hrs earlier.the distance traveled by person ?
a. 55 km b. 60 km c. 65 km d. 70 km
Sol: D = (2*5*7.5*2)/(7.5-5) = 60 km
If a body covers part of the journey at speed p km/hr and the remaining part of the journey at a speed q km/hr and the distances of the two parts of the journey are in the ratio m : n, then the average speed for the entire journey is
= (m+n) pq / (mq+np).
Ex: If a Manish covers part of the journey at speed 2 km/hr and the remaining part of the journey at a speed 4 km/hr and the distances of the two parts of the journey are in the ratio 3 : 2, then the average speed for the entire journey ?
a. 5 b. 2.5 c. 10 d. 7.5
Sol: = [(3+2)*2*4] / [(3*4)+(2*2)]
= 2.5 km/hr
A train travelling at a speed of 'S1' kmph leaves A at 't1' hrs. and another train travelling at speed 'S2' kmph leaves A at 't2' hrs in the same direction. Then the meeting point's distance from starting is given by = (S1 xS2 X Difference in time) /Difference in speed.
Ex: A train travelling 25 kmph leaves Delhi at 9 a.m. and another train travelling 35 kmph starts at 2 p.m. in the same direction. How many km from will they be together ?
a. 437.5 b. 137.5 c. 237.5 d. 337.5
Sol : Meeting point's distance from the starting point = [25 x35 x(2p.m. - 9 a.m)] / (35 -25) = (25 x35x 5) / 10 = 4375 / 10 = 437.5 km .