Question

A car moving on a straight road covers the one-fourth of the total distance with 36 km/h and the rest with 54 km/h, the average speed of the car is

Answer 1

Given :- A car moving on a straight road covers the one-fourth of the total distance with 36 km/h and the rest with 54 km/h, the average speed of the car is ?

Answer :-

Let us assume that, Total distance covered by car is 40x km .

so,

→ (1/4)th distance = 10x km

→ Rest distance = 30x km .

now,

→ Time taken to cover (1/4) distance = Distance/speed = 10x/36 = (5x/18) hours.

and,

→ Time taken to cover rest distance = D/S = 30x/54 = (5x/9) hours .

then,

→ Total time taken = (5x/18) + (5x/9) = (5x +10x)/18 = (15x/18) = (5x/6) hours .

therefore,

→ Average speed = Total distance covered / Total time taken = 40x / (5x/6) = 40x * (6/5x) = 48 km/h (Ans.)

LCM Method :-

LCM of 36 and 54 = 108 km = Let total distance covered .

so,

→ Distance covered at 36 km/h = (1/4)th of total = (1/4) * 108 = 27 km .

then,

→ Time taken by car = Distance/speed = (27/36) = (3/4) hours .

similarly,

→ Distance covered at 54 km/h = Rest distance = 108 - 27 = 81 km .

then,

→ Time taken by car = Distance/speed = (81/54) = (3/2) hours .

therefore,

→ Average speed = Total distance covered / Total time taken = 108/(3/4 + 3/2) = 108/(9/4) = 108 * (4/9) = 48 km/h .

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Answer 2

Given : A car moving on a straight road covers the one-fourth of the total distance with 36 km/h and the rest with 54 km/h,

To Find : the average speed of the car  

Solution:

Let say total Distance = 4D km

one-fourth of the total distance = D km

Speed = 36 km/hr

Time = D/36   hr

rest distance = 4D - D = 3D km

Speed = 54 km/hr

Time = 3D/54  = D/18   hr

Total Time = D/36  + D/18

= (3D)/36

= D/12

Average speed  = 4D/(D/12)   =  48 km/hr

Average speed   of  the Car = 48 km/hr

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