A reaches 0 to P with a speed of 5 km per hr. Again, A came back to P from 0 with a speed of 6 km per hr. A needs 11/2 hours in total. Form an equation letting the distance from O to P be x.

Question

Here,i would like to ask if 6 km could be counted as distance here. If so,why? I learnt that when addressed as "6 km per hour" it should be counted as speed in a whole.

Answer 1

Speed always involves distance and time, so you can't treat 6km alone as a distance without considering time. Hence the use of the relationship x=vt below.

x=vt where v=speed and t=time. Let t₁ be the time to go from O to P and t₂ the time to return to O from P, then t₁=x/5 and t₂=x/6. The total time t=t₁+t₂=x/5+x/6=11/2.

So the equation is x/5+x/6=11/2.

To solve it:

(6x+5x)/30=11/2,

11x/30=11/2,

x/30=½,

x=30/2=15km.

(Knowing x=15km, we can see it takes 15/5=3 hours to go from O to P, and it takes 15/6=5/2=2½ hours to go from P to O. Add these times together: 5½ hours = 11/2 hours.)