Example 6 :
With a uniform speed a bike covers the distance in 10 hours . When speed of bike is increased by 4 km / hr , the same distance could have been covered in 8 hours . What is the distance covered by bike ?
Answer :
let the distance be x km . Then ,
x / 8 – x / 10 = 4
x = 160 km .
Example 7:
A Car covers a certain distance in 7 hours at the speed of 73 Kms/hr. What is average speed of bus? Which travels a distance of 55 Kms. less than the car in the same time ?
Answer :
Step 1 : The distance coverd by the bus = ( 73 x 7 ) = 511
Step 2 : The distance cover bus = 511 – 55 = 456 Km. So average speed of the bus = 456 / 7 = 65.14Km/hr.
Example 8:
A civik car covers 258 Kms, in 3 hours. The average speed of a bike is 45% more than the average speeed of the car. How much distance will the bike cover in 6 hours ?
Answer :
Step 1: Speed = 258 / 3 = 86.
Step 2: 86 x 145 / 100 = 124.7 Distance = 124.7 x 6 = 748.2 Km
Example 9:
The ratio between two super fast trains is 6 : 8. if the second train runs 600 Kms in 6 hours, then what would be the speed of the first train ?
Answer :
Step 1: Let the speed of two trains be 6x and 8x Km /hr.
Then, then we find the value of x,
8x = 600 / 6 = 100
x = 100 / 8 = 12.5.
here is value of x is 12.5 we put in first train.
Step 2: Speed of first would be = ( 6 x 12.5 ) Km / hr = 75 Km / hr.
So the Speed of First train is 75 Km / hr.
Example 10 :
A boy without any stoppage running on a road at an average speed of 80 km /hr , and with stoppage he covers the same distance at an average speed of 60 km / hr . How many minutes per hour does boy stop ?
Answer :
Let the total distance cover by boy on road is x km .
Time take to complete at a speed of 80 km / hours = x / 80 hours .
Time take to complete at a speed of 80 km / hours = x / 60 hours .
So he stop to rest ( x / 80 – x / 60 ) hours = 20x / 60 x 80 = x / 240 hours .
So he rest per hour = x / 240 / x / 60 = x / 240 x 60 / x = 1 / 4 hours = 15 minutes .
Shortcut Tricks :
Time of rest per hour = ( Difference of speed / Speed without stoppage )
( 80 – 60 ) / 80 = 1 / 4 = 15 minutes
Example 11:
A man walking at the rate of 4kmph to cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in what time?
Answer:
we know the formula of
Distance = speed x Time
So, Time given = 2hr 45min = 2x60min+45min=165min than 165min / 60min = 11 / 4 hr
Distance = 4 x 11 / 4 = 11 km
So, Time required to cover distance in speed of 16.5kmph
Time = D / S = 11 / 16.5 = 40min.
Example 12:
A fast train covers a distance in 40 min, if it runs at a speed of 45kmph on an average. The speed at which the train must run to reduce the time of journey to 30min will be?
Answer:
Time = 40 / 60 = 2 / 3.
given speed = 45kmph
Distance = Speed x Time.
Distance = 45 x 2 / 3 = 30km
Time =30 / 60 = 1 / 2hr
Speed = Distance / Time.
So, the new speed is = 30 x 2 = 60kmph
Example 13:
A train traveling at 90 kmph overtakes a bike traveling at 54 kmph in 30 seconds. What is the length of the train in meters?
Answer:
The distance travailed by the train overtaking the bike is the same as the length of the train.
both the object move in same direction .
so, ( 90 – 54 ) = 36kmph
convert kmph to m/sec = 36 x 5 / 18 = 10 m / sec.
Time taken in 40 sec.
distance travailed = 10 x 30 = 300 meters.
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