Important Formulas
- Speed = Distance / Time
- Time = Distance / speed
- Distance = speed x time
If the ratio of the speed of A and B is a:b, then the ratio of the time taken by them to cover the same distance is 1/a : 1/b or b:a
Suppose a man covers a distance at x km/h and an equal distance at y km/h. then the average speed during the whole journey is (2xy/x+y) km/h
An object that moves at a constant rate is said to be in uniform motion.
The formula d = rt gives the relationship between distance d, rater, and time t.
Uniform motion problems may involve objects going in the same direction, opposite directions, or round trips.
Examples:
1. Walking at the rate of 4 km/h a man covers a certain distance in 2 hr 45 min. Running at a speed of 16.5 km/h the man will cover the same distance.
Solution:
Distance = Speed x time
4x(11/4) = 11km
New Speed = 16.5 km/h
Therefore time = D/S = 11/16.5 = 40 min
2. A train covers a distance in 50 min if it runs at a speed of 48 km/h on average. The speed at which the train must run to reduce the time of journey to 40 min will be.
Solution:
Time = 50/60 hr = 5/6hr
Speed = 48 m/h
distance = S x T = 48 x 5/6 = 40 km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 km/h = 60 km/h
3. Two boys starting from the same place walk at a rate of 5 km/h and 5.5 km/h respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?
Solution:
The relative speed of
the boys = 5.5 km/h – 5km/h = 0.5 km/h
Distance between them is 8.5 km
Time= 8.5km / 0.5 km/h = 17 hrs
4. In covering a distance of 30 km, Saad takes 2 hours more than Rohan. If Saad doubles his speed, then he would take 1 hour less than Rohan. Saad speed is?
Solution:
Let Saad’s speed be X km/hr.
Then, 30/x – 30/2x = 3
6x = 30
x = 5 km/hr.
5. A train 140 m long running at 60 kmph. In how much time will it pass a platform 260 m long?
Solution:
Distance travelled = 140 + 260 m = 400 m,
Speed = 60 x 5/8 = 50/3 m
Time = 400 x 3/50 = 24 Seconds
Time and Work
Work is the quantity of energy transferred from one system to another but for question based on this topic. OR Problems on work are based on the application of the concept of the ratio of time and speed.
Above mentioned definition of work throws light on three important points.
- Work = 1 ( as it is always measured as a whole) = Distance
- Rate at which work is done = speed
- Number of days required to do the work = Time
Formulas:
- Work from Days: If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
- Days from Work: If A’s 1 day’s work = 1/n then A can finish the work in n days.
Examples:
1. If 5 women or 8 girls can do work in 84 days. In how many days can 10 women and 5 girls can do the same work?
Solution:
Given that 5 women is equal to 8 girls to complete a work.
So, 10 women = 16 girls.
Therefore 10 women + 5 girls = 16 girls + 5 girls = 21 girls.
8 girls can do a work in 84 days then 21 girls can do a work in (8 x 84/21) = 32 days.
Therefore 10 women and 5 girls can a work in 32 days
2. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Solution:
A’s one hour work = 1/8. B’s one hour work = 1/10.
(A+B)’s one hour work
= 1/8 + 1/10 = 9/40. Both A & B can finish the work in 40/9 days.
3. A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?
Solution:
Given that B alone can complete the same work in days = half the time taken by A
half the time taken by A = 9 days
A’s one day work = 1/18
B’s one day work = 1/9
(A+B)’s one day work = 1/18 + 1/9 = 3/18 = 1/6
4. A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
Solution:
If A takes x days to do a work then B takes 2x days to do the same work
= 1/x + 1/2x = 1/18
= 3/2x = 1/18
x = 27 days.
Hence, A alone can finish the work in 27 days.
5. A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
Solution:
Ratio of time taken by A & B = 160 : 100 = 8 : 5
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 12 : x
= 8x = 5 x 12
= x = 15/2 days.