Time and Speed
1. Distance = Speed * Time
2. Speed = Distance / Time
3. Time = Distance / Speed
4. 1 km/h = 5/18 m/sec
5. 1 m/sec = 18/5 km/h
Example:
1. Rita covers a certain distance by a car traveling at a speed of 70 km/h and returns at the starting point riding on a scooter at the speed of 55 km/h. Find her average speed for the whole journey.
Average Speed = (55 + 70)/2 = 62.5 km/h
2. Ram starts from his house for the college at a certain fixed time. If he walks at the rate of 5 km/h he is late by 7 minutes. However, if he walks at the rate of 6 km/h he reaches the college 5 minutes earlier than the scheduled time. Find the distance of the college from his house.
Suppose the distance is x km.
If he goes by 5km/h then x/5 - 7/60 = x/6 + 5/60.
therefore x/30 = 1/5
so x = 6km
Relative Speed
Two bodies are moving in opposite directions at speed V1 & V2 respectively. The relative speed is defined as Vr = V1 + V2.
Two bodies are moving in same directions at speed V1 & V2 respectively.The relative speed is defined as Vr = V1 - V2.
Clock Problems
For clock problems consider the clock as a circular track of 60km.
Min. hand moves at the speed of 60km/hr (think min. hand as a point on the track) and hour hand moves at 5km/hr and second hand at the speed of 3600 km/hr.
Relative speed between hr hand and mins hand = 55
Examples
1. A man travels a distance of 61 km in 9 hours partly on foot at the rate of 4 km/h and partly on bicycle at 9 km/h. How much distance does he cover on foot?
Solution
Let the distance covered on foot be x.
Then the distance covered by bicycle is 61 -x.
The total distance is covered in 9 hours.
Time for which the man travels by foot = Distance/ velocity = x/4 hrs
Time for which the man travels by bicycle = (61 -x) / 9 hrs
x/4 + (61 - x)/9 = 9
9x + 244 -4x = 9
36
5x = 324 -244
x = 16 km
2. A 75 m long train moving at 60 km/h can pass another train 100 m long, moving at 65 km/h in the opposite direction in:
Solution
Such problems can be solved using the formula velocity = distance/time. It's necessary to make sure that similar units are used in the formula.
To completely pass each other, the trains have to cover a distance equal to the sum of the Iengths of the two trains, 75 + 100 = 175 mtrs.
When travelling in opposite directions, the velocity with which this distance gets covered is the sum of the two velocities. 60 + 65 = 125 Kmph or 125 * 1000 mtrs per 60 * 60 Secs or 625/18 mtrs/sec.
Therefore time to cross each other = 175 = 5.04 secs.
3. Find the speed of the current if a boy rows 13 km upstream and 28 km downstream taking 5 hours each time.
Solution
Let the speed of the current be x km/hr and that of the boy when he rows in still water be y km/hr.
Then the relative speed when the boy rows upstream = y -x km/hr
The relative speed when the boy rows downstream = y + x km/hr
The time taken for the 13 km long upstream journey is 5 hours. Therefore we can write this as
Speed = Distance/Time
y -x = 13/5 ------ I
The time taken for the 28 km long downstream journey is also 5 hours, therefore
y + x = 28/5 ----- II
Subtracting equations II from equation I, we obtain,
2x = 28/5 -13/5
2x = (28 -13) / 5
2x = 15/5
x = 3/2 = 1.5 km/hr, the speed of the current
Assignment
1. Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph. While the other man travelled with varying speeds as follows: In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on. When will they meet each other?
2. A man travels three-fifths of distance AB at a speed of 3a, and the remaining at a speed of 2b. If he goes from B to A and back at a speed of 5c in the same time, then:
[1] 1/a + 1/b = 1/c [2] a + b = c [3] 1/a + 1/b = 2/c [4] None of these
3. A man travels form A to B at a speed of x kmph. He then rests at B or x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to 12 km, the time for which he rested at B could be:
4. In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs 18 min 15 seconds of watch time. What is the time gained or lost by this watch in one day?
5. In a mile race Akshay can be given a start of 128 metres by Bhairav. If Bhairav can given Chinmay a start of 4 metres in a 100 metres dash, then who out of Akshay and Chinmay will win a race of one and half mile, and what will be the final lead given by the winner to the loser? (One mile is 1600 metres).
DIRECTIONS for Questions 6 and 7: In a locality, there are five small towns, A, B, C, D and E. The distances of these towns from each other are as follows:
AB = 2km AC = 2 km AD > 2 km AE > 3 km BC = 2km
BD = 4 km BE = 3 km CD = 2 km CE = 3km DE > 3 km
6. If a ration shop is to be set up within 2 km of each city, how many ration shops will be required?
7. If a ration shop is to be set up within 3 km of each city, how many ratio shops will be required?
