Time and Distance Tricks, Time and Distance Shortcuts

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Time and Distance Formula :-

Time and Distance Shortcuts:-

Time and Distance Tricks 1:- If a person travels half a distance in a journey at x km/hr and remaining half at the speed of y km/hr, the average speed of the whole journey is given by:

Example 1

A person travels half of journey at the speed of 30 km/hr and the next half at a speed of 15 km/hr. What is the average speed of the person during the whole journey?

Here; x= 30 and y= 15 Putting the in above formula the Answer will be= 20 km/hr

Time and Distance Tricks 2:- If a person travels three equal distances in a journey at a speed of x km/hr, y km/hr and z km/hr. The average speed is given by:

Example 2

Rajesh starts from Faizabad to Lucknow a distance of about 300 kms. He divided his journey into a distance of thee equal parts in terms of distance and covered them with the speed of 30 km/hr, 60 km/hr and 90 km/hr, calculate his average speed during the journey:

Here: x= 30, y= 60, z= 90. Putting the values we get: Answer= 49.09 km/hr

Time and Distance Tricks 3:- If a person travels Mth part of a distance at x km/hr, Nth part at y km/hr and the remaining Pth part at z km/hr, Then his average speed in km/hr is given by:

If instead of proportion, the parts of the distance are given in percentage i.e. M%, N% and P% respectively, then the formula becomes:

Example 3

Hari travels 20% of a distance at an average speed of 20 km/hr, next 30% distance at an average speed of 30 km/hr and the remaining 50% of distance at the average speed of 50 km/hr. Find his average speed during the whole journey.

Sol: Here M=20, N=30 and P= 50 also x= 20, y= 30 and z= 50

Putting the values we get: Answer =33.33 km/hr

Time and Distance Tricks 4:- If a car does a journey in ‘T’ hrs, the first half at ‘a’ km/hr and the second half at ‘b’ km/hr. The total distance covered by the car:

(2 x Time x a x b ) / (a + b).

Example:- A motorcar does a journey in 10 hrs, the first half at 21 kmph and the second half at 24 kmph. Find the distance?
Sol: Distance = (2 x 10 x 21 x 24) / (21+24)
= 10080 / 45
Answer = 224 km.

Time and Distance Tricks 5 .If a person goes from ‘A’ to ‘B’ at a speed of ‘a’ kmph and returns at a speed of ‘b’ kmph and takes ‘T’ hours in all, then the distance between the A and B:

= Total time taken x (Product of the two Speeds / Addition of the two speeds)

Example: A boy goes to school at a speed of 3 kmph and returns to the village at a speed of 2 kmph. If he takes 5 hrs in all, what is the distance between the village and the school?

Sol: Let the required distance be x km.
Then time taken during the first journey = x/3 hr.
and time taken during the second journey = x/2 hr.
x/3 + x/2 = 5 => (2x + 3x) / 6 = 5
=> 5x = 30.
=> x = 6
required distance = 6 km.

Time And Distance Solved Example

Ex .An aeroplane files along the four sides of a square at the speeds of 200,400,600 and 800km/hr.Find the average speed of the plane around the field.
Sol. :
Let each side of the square be x km and let the average speed of the plane around the field by y km per hour then ,
x/200+x/400+x/600+x/800=4x/y=25x/2500=4x/y=y=(2400*4/25)=384 hence average speed =384 km/hr

Ex. If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
Sol. Let the required distance be x km
Difference in the time taken at two speeds=1 min =1/2 hr
Hence x/5-x/6=1/5<=>6x-5x=6 =x=6
Hence, the required distance is 6 km

Ex. A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
Sol. Suppose they meet x hours after 10 a.m. Then,

(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x = 17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.

Ex. I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?
Sol. Let the distance be x km. Then,
( Time taken to walk x km) + (time taken to ride x km) =37 min.
( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min.
But, the time taken to walk 2x km = 55 min.
Time taken to ride 2x km = (74-55)min =19 min.

Time and Distance Quiz

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