Question

1. A nonstop bus goes from one station to anothers tation with a speed of 54 km/h. The same bus retum from the
second station to the firststation with a speed of 36 km/h. Find the average speed of the bus for the entire jou me
2. A train travels 20 kmata uniform speed of 60 km/h and the next 20 km at the uniform speed of 80 km/h. Calculas
it average speed.​

Answer 1

Question 1:

A nonstop bus goes from one station to another station with a speed of 54 km/hr. The same bus return from the second station to the first station with a speed of 36 km/hr. Find the average speed of the bus for the entire journey.

Answer:

$\bigstar{\bold{Average\:speed\:=43.2\:km/hr}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Speed in the first case = 54 km/hr
• Speed in the second case = 36 km/hr

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Average speed

$\Large{\underline{\underline{\bf{Solution:}}}}$

➳ Let the distance between the stations be x km

➳ Hence,

    The total distance travelled = 2x km

➳ We know that,

    Time = Distance/Speed

➳ Time for first case = x/54 hours

➳ Time for second case = x/36 hours

➳ We know that,

    Average speed = Total distance/Total time

➳ Substitute the data,

    Average speed = 2x/(x/54 + x/36)

    Average speed = 2x/(90x/1944)

    Average speed = 2x × 1944/90x

    Average speed = 43.2

➳ Hence the average speed is 43.2 km/hr

    $\boxed{\bold{Average\:speed=43.2\:km/hr}}$

Question 2:

A train travels 20 km at a uniform speed of 60 km/hr and the next 20 km at a uniform speed of 80 km/hr

Answer:

$\bigstar{\bold{Average\:speed=70\:km/hr}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Train covers 20 km at a speed of 60 km/hr
• Train covers 20 km at a speed of 80 km/hr

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Average speed

$\Large{\underline{\underline{\bf{Solution:}}}}$

➺ Here total distance is given by,

    Total distance = 20 + 20 = 40 km

➺ In the first case,

   Time taken = Distance/Speed

    Time taken = 20/60

    Time taken = 0.33 hour

➺ In the second case,

   Time taken = 20/80

   Time taken = 0.25 hour

➺ Hence,

    Total time taken = 0.33 + 0.25 = 0.58 hours

➺ Now,

    Average speed = Total distance/Total time

    Average speed = 40/0.58

    Average speed = 70 km/hr

➺ Hence the average speed is 70 km/hr

    $\boxed{\bold{Average\:speed=70\:km/hr}}$

Answer 2

Answer :-

★ Concept :-

Here the concept of Average Speed has been used. Average Speed is equal to the total distance travelled by the object divided by the total time taken to cover that distance. This is given as :-

• Average Speed = Total Distance /Total Time

• Time = Distance / Speed

_____________________

★ Solution :-

1.) A nonstop bus goes from one station to another station with a speed of 54 km/h. The same bus return from the second station to the firststation with a speed of 36 km/h. Find the average speed of the bus for the entire journey.

________________________________

Given,

• Speed for going = 54 Km/hr

• Speed for returning = 36 Km/hr

» Let the total distance covered in returning be 'x' Km. Then total distance covered in returning is equal to total distance covered while going.

Then, by using relation between Time, Distance and Speed, we get,

▶Time taken for going = (x/54) hr

▶Time taken for returning = (x/36) hr

▶ Total time for journey = {(x/54) + (x/36)} hr

▶Total distance of journey = x + x = 2x

Equating these values in the formula of Average Speed, we get,

✒ Average Speed = 2x / {(x/54) +(x/36)}

✒ Average Speed = 2x / (90x/1944)

✒ Average Speed = (2x × 1944) / 90

✒ Average Speed = 43.2 Km/hr

________________________________

✳ Hence, average speed of the journey =

43.2 Km/hr

_____________________

_____________________

2.) A train travels 20 km with uniform speed of 60 km/h and the next 20 km at the uniform speed of 80 km/h. Calculate its average speed.

_______________________________

Given,

• Train covers first 20 Km at = 60 Km/hr

• Train covers second 20 Km at = 80 Km/hr

• Total distance covered = 20 + 20

= 40 Km

Then, using the relationship between speed, time and distance we get,

▶Time taken to cover first 20 Km = 20/60 = 0.33 hr

▶Time taken to cover second 20 Km = 20/80 = 0.25 hr

▶ Total time taken = 0.33 + 0.25

= 0.58 hr

Now by applying the values in the formula of average speed, we get,

✒ Average Speed = 40/(0.58)

✒ Average Speed = 70 Km/hr

✳ Hence, we get, the average speed for the entire journey = 70 Km/hr

_____________________

★ More to know :-

• Speed is the rate of change of position of the body in any direction.

• Uniform Speed is the speed of an object if the object is moving with uniform speed and if it covers equal distances in equal intervals of time.

• Instantaneous Speed is the speed of an object at any particular instant of time or at a particular point.

• Variable Speed is the speed of an object if the object is moving with non - uniform speed and if it covers unequal distances in unequal intervals of time.