SOLUTION: 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

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Question 1054641: 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?

This question is of TIME,SPEED & DISTANCE chapter
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
The order in which each agent starts its trip is P, Q, R. The agent traveling for the shortest time will be R.

Interesting no time values are given; only variables must be kept for all numbers. 

                 RATE         TIME        DISTANCE

P begins          a           t+p           d

Q begins         a+b          p             d

R begins         a+2b         x             d


We can only expect we do NOT know d, t, or x. We know none of them. We should assume a, a+b, a+2b, and p are constants, although not given other than as those variables.

Based on constant travel rate rule, RT=D we can form a system of equations.


The question asks essentially for solution to x. Could you try to solve for d, first, and use it to solve for x? Did you possibly miss any given information from your problem description?

I see only this at best:
and the only unknown variable is x.
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