__Speed, Time and distance__

__Basic Formula of speed and distance__

**Distance****=**Speed x Time**Speed****=**Distance / Time**Time****=**Distance / Speed

**1 km. /hour** = m. /sec

**1 m. /sec** = km. /hour

__Example:__

Arjun goes to his college from his house at a speed of 3 Km / hr and return at speed of 2 km / hr. If he takes 5 hours in going and coming, the distance between his house and college is-

__Answer:__

Average speed = ( ) km / hr = km / hr.

**Distance between his house and college he travelled : (** **x 5 ) km = 12 km .**

__Example:__

How many minutes does Seema take to cover a distance of 600 m, if she runs at speed of 40 km / hr ?

__Answer:__

Seema speed = 40 km / hr,.

(40 x ) = m / sec (after converting it into m / sec)

So, Seema Time taken to cover 600 m = (600 x ) sec = 54 sec.

**So ****Seema Time taken to cover distance 54 sec.**

__Example:__

Harish on tour travels first 160 km at 64 km /hr and the next 160 km at 80 km /hr . The average speed of for the first 320 km of the tour is :

__Answer:__

Total time taken by Harish is : = ( + ) hrs = hrs .

So **that Average speed = (320 x** **) km / hr = 71.11 km / hr **

__Example:__

A car completes a journey in 12 hours , the first half hours complete at 23 km / hr and the second half at 25 km / hr . Find the distance?

__Answer:__

let the distance be x km .

Time taken by the car to complete the km at a speed of 23 km / hr

the car has time taken to complete the km at a speed of 25 km / hr

So , total time taken to complete the whole journey is ,

= 23 + 25 = 10 hrs

x =

x =287.5

**Shortcut tricks:** Distance = Here S_{1} = speed during first half and S_{2} = Speed of second half of journey

**Distance = ** **= 287.5 km .**

__Example:__

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 ,

– = 4

**x = 160 km .**

__Example:__

A Truck 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 Truck in the same time?

__Answer:__

**Step 1 :** The distance covered by the Truck = ( 73 x 7 ) = 511

**Step 2 :** The distance cover bus = 511 – 55 = 456 Km.

So, average speed of the bus = = 91.2 Km/hr.

__Example:____ __

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 = = 100

x = = 12.5.

Here, 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:__

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 ( – ) hours = = .

So he rest per hour = / = ( ) x ( ) = hours = 15 minutes.

__Shortcut Tricks:__

Time of rest per hour = ( Difference of speed/ Speed without stoppage )

= = 15 minutes

__Example:__

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:__

By the formula of **Distance = speed x Time**

So, Time given = 2hr 45min = 2x 60min+ 45min= 165min

= hr

Distance = 4 x = 11 km

So, Time required to cover distance in speed of 16.5kmph

Time = D / S = 11 / 16.5 =** ****40min.**

__Example:__

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 = 10 m / sec.

Time taken in 40 sec.

distance travailed = 10 x 30 = 300 meters.