Question

A and B run a 1 km race. If A gives B a start of 50 m and still beats him by 15 seconds, and if A gives B a start of 70 m and beats him by 10 seconds, find the time taken by A to run 1 km.

• A. 100 seconds
• B. 120 seconds
• C. 150 seconds
• D. 180 seconds

Hint:

Solve race problems by setting up time equations based on distances and solving simultaneously.

Answer 1

The Correct Option is A

Let A’s speed = \( v_A \) m/s, B’s speed = \( v_B \) m/s, A’s time = \( t_A \) seconds. 
Case 1: B runs 950 m in \( t_A + 15 \) seconds: 
\[ \frac{950}{v_B} = t_A + 15 \] Case 2: B runs 930 m in \( t_A + 10 \) seconds: 
\[ \frac{930}{v_B} = t_A + 10 \] Divide equations: 
\[ \frac{950}{930} = \frac{t_A + 15}{t_A + 10} \Rightarrow 950(t_A + 10) = 930(t_A + 15) \] \[ 950t_A + 9500 = 930t_A + 13950 \Rightarrow 20t_A = 4450 \Rightarrow t_A = 100 \] Thus, A takes 100 seconds.