Calculating P's Race Time with Head Start

The problem involves calculating the time taken by P in a race, considering a head start given to Q and their respective speeds.

1. Calculate Q's Time

First, find the time Q takes to complete the 600 m race.

• Distance = 600 m
• Speed of Q = 4 m/sec
• Using the formula: Time = Distance / Speed
• Time for Q, denoted as $T_Q$: $ T_Q = \frac{600 \text{ m}}{4 \text{ m/sec}} = 150 \text{ seconds} $

2. Relate P's and Q's Times

P gives Q a 10-second head start, and they finish the race simultaneously.

• This means Q starts 10 seconds earlier than P.
• Since they finish at the same time, P runs for 10 seconds less than Q.
• Let $T_P$ be the time taken by P.
• The relationship is: $ T_Q = T_P + 10 \text{ seconds} $

3. Calculate P's Time

Substitute the value of $T_Q$ into the equation.

• $ 150 \text{ seconds} = T_P + 10 \text{ seconds} $
• $ T_P = 150 \text{ seconds} - 10 \text{ seconds} $
• $ T_P = 140 \text{ seconds} $

Therefore, the time taken by P to finish the race is 140 seconds.

The correct answer corresponds to Option A.