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 is pa/a+2b
Your faculty have posted the answer but I didn't get some part of the answer properly and in that answers how i come to know that we have to take T and t-p and t-p-x and one request is that can you explain question properly
To understand the answer to the question, let's break it down step by step.
We have three people: P, Q, and R. They start from the same place, X. The respective speeds of P, Q, and R are a kmph, (a+b) kmph, and (a+2b) kmph.
Let's assume that P starts at time t=0. We need to find out at what time P, Q, and R will meet.
Since P starts at time t=0, Q starts p hours after P. Therefore, Q starts at time t=p.
To find when Q and P will meet, we need to calculate the distance they travel until they meet. The distance traveled is equal to speed multiplied by time. Since P is traveling at a kmph, the distance traveled by P is a * t.
Similarly, the distance traveled by Q is (a+b) * (t-p), because Q starts p hours after P.
Now, to find when Q and P meet, we set their distances traveled equal to each other and solve for t:
a * t = (a+b) * (t-p)
Simplifying this equation, we get:
at = at - bp + bt
Canceling at from both sides, we get:
0 = -bp + bt
Rearranging the equation, we get:
bp = bt
Dividing both sides by b, we get:
p = t
So, we find that Q and P will meet at time t=p.
Now, let's find out when R needs to start so that both Q and R overtake P at the same time.
Since Q starts p hours after P, R needs to start at time t = p + (t-p). Simplifying this equation, we get:
t = p + (t-p)
t = t - p + p
Cancelling out t and p from both sides, we get:
0 = -p + p
Therefore, R needs to start p hours after Q starts.
Now, if we substitute t = p in the equation, we get:
t = p
t = pa/a+2b
So, the answer is pa/a+2b.