Question

1/3 of a certain journey is covered at the rate of 25km/h,1/4 at the rate of 30km /h and the rest of 50km/h.what is the average speed for the whole journey​

Answer 1

Step-by-step explanation:

Let the total distance be x km.

1/3rd of the journey is travelled at a speed of 25 km/hr

We know that, Speed = Distance / Time

So, time taken to travel first x/3 km, t1

= Distance / Speed = (x/3)/ 25 = x/75 hour

1/4th of the journey is travelled at 30 km/hr

Time taken to travel x/4 km, t2

= Distance / Speed = (x/4)/ 30 = x/120 hour

The remaining journey is travelled at 50 km/hr

x/3 + x/4 = (4x+3x)/12 = 7x/12 km

x – 7x/12 = 5x/12 km

Time taken to travel 5x/12 km, t3

= Distance / Speed = (5x/12)/ 50 = 5x/600 hour

Total time taken = t1 + t2 + t3

= x/75 + x/120 + 5x/600 = (8x + 5x + 5x)/600 = 18x/600 hour

Total distance travelled = x km

So, average speed = Total distance / Total time = x/(18x/600) = 600x/18x = 33.33 km/h

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