Aptitude - Time and Distance - Discussion

Use average speed formula 2xy/x+y and multiply with time.

Since Distance = Time*Speed.

I can't understand this problem. Please explain.

There said half the journey. So why didn't we get half the time for calculation.

Like (5*24)+(5*21) = 225.

Simple trick.

Find average speed because they are given half and half journey.

2xy/x+y......> 2(21)(24)/(21+24).

So average speed = 2(21)(24)/45.

Therefore D = S*T.

= [2(21)(24)/45]*10 = 224.

Average speed = (2*21*24)/(21+24) = 102/5.

Distance = (102*10)/5 = 224.

Following is explanation:

Total Travel Time = 10 hours.

Let's assume Total Distance = d kms and 1st half (i.e d/2) was completed in x hours at speed of 21 kmph.

=> d/2 = 21x.

=> d/42 = x.....equation (1).

=> 2nd half (i.e d/2) was completed in (10-x) hours @ speed of 24 kmph.

=> d/2 = 24*(10-x).
=> d/48 = 10-x.

=> x = 10-(d/48)....equation (2).

From equation (1) and (2),

=> d/42 = 10-(d/48).
=> d/42 + d/48 = 10.
=> d = 2*5*2*3*7*8/(3*5).
=> d = 224 kms.

First half of journey means half distance of journey. Not half ours of time. May it will help you.

To apply formula 2uv/(u+v),

Where,

s = Distance;

u = First Half velocity which is 21 kmph.

v = Second Half Velocity which is 24 kmph.

=> (2*21*24)/(21+24).

=> (1008)/45.

=>22.4 kmph.

Therefore, average speed = 22.4 km/hr.

s = vt.
s = 22.4 km/hr x 10hrs.
s = 224 km.

I ll tell you people the easiest method.

Average speed = 2xy/(x+y) = 22.4.

Time is given 10 hrs.

So 10x22.4 = 224.

How does 15x arrived?