What is the total distance traveled by Pramod in km for 14 Hours 40 Min?

Question

Pramod travels for 14 hours 40 min. He covers one half of the journey by train at 60 kmph and the rest half by road at 50 kmph. What is the total distance traveled by Pramod (in km)

Answer 1

Let's total time=t=14hrs 40 min=880 min............(i)
total distance travelled=x
half distance=d1=d2=x/2........................................(ii)
Speed=s1=60km/hr=1km/min..............................(iii)
s2=50km/hr=50/60 km/min.................................(iv)
t=d/s=[(d1/s1)]+[(d2/s2)]
880=[(x/2)/1]+[(x/2)/(50/60)]................from (i) to (iv)
x=800
ans is 800 km

Answer 2

Let the 2 halves of the distances be d
Then travel by train time t1=d/60
travel by road time t2=d/50
Total time = d (110/3000) = t1+t2
Now total distance/ total time = average speed
2d/(d (110/3000)) = 600/11km/hr
Now required distance = av speed x time
= (600/11)×(44/3) = 800 km

Answer 3

14.667x(60+50)/2 = 14.667x55 = 806.6685 km

Comments

You cannot take the average speed to be 55 as he is travelling at 60 for a little less time compared to when he is travelling at 50, even though they are travelling in both the cases the same distance.

So in other words while measuring average speed we have to check for how long what speed was maintained into the calculation.

The average speed in this case turns out to be 54.54 just a little less than what you came up with hence the slight error.