Question

Acar moves from city A to B on a straights line and then comes back. While moving from A to B it covers first half of the distance at rate of 40km/hr and next half with 60km/hr while moving back from B to A it moves with 40km/hr for half time and 60km/hr for remaining half time. Find the average speeds for complete motion A to B and back to A ?

Answer 1

Dear student,

Let the distance between A and B be x. And the time taken on the return journey from B to A be T.

On the journey A to B, half distance was covered at speed 40 kmph and next half in 60 kmph.

Time taken to cover half distance:
Distance/speed= (x/2)/40
= x/80 hour.

Time taken to cover next half:
=(x/2)/60= x/120 hour.

Total time taken for journey from A to B
= x/80 + x/120
= 3x/240 + 2x/240
= 5x/240
= x/48

In the returning journey, the first half of time was travelled at 40 kmph and next half time in 60 kmph.

So, distance covered at
40 kmph:
= Distance= speed×time
= 40×(T/2)
= 20T km.

Distance covered at 60 kmph
= 60× (T/2)
= 30T km.

Distance from B to A
= x= 30T + 20T
= x= 50T
T = x/50


Average speed
= total distance/ total time

Total distance= 2x
Total time= x/48 + T
= x/48+ x/50
= 98x/2400

Average speed
=( 2x)/( 98x/ 2400)

= (2x × 2400)/98x

= 4800/98
= 48.97 kmph
≈49 km/h

49kmph= 13.61 m/s.