Question

P, Q and R start from the same place X at (a) kmph, (a+b) kmph and (a+2b) kmph respectively.

If Q starts p hours after P, how many hours after Q should R start, so that both Q and R overtake P at the same time?

Answer 1

Velocity = distance/time
P=a = x/t1
Q=a+b = x/t2
R=a+2b = x/t3

Q stats p hours after P:

(a+b)=X/(t1+p)

hours after Q should R start:

a+2b = X/(t2+h)

t1=x/a

t2=t1+p
t3=t1+p+h

Velocity Q = R
by manipulating the velocity formula:

Velocity/time = distance

Q distance = R distance

Velocity*time=distance:



(a+b)/(t1+p) = (a+2b)/(t1+p+h)

solve for h:

Answer 2

t1+p = t2

so:

(a+b)/t2 = (a+2b)/(t2+h)

h= ((a+2b)*t2)/(a+b) - t2

h=b*t2/(a+b)