Question

two runners start at the same point and jog at a constant speed along a straight path. runner a starts at time t = 0 s, and runner b starts at time t = 2.5 s. the runners both reach a distance 64 m from the starting point at time t = 25 s. if the runners continue at the same speeds, how far from the starting point will each be at time t = 45 s? runner a will be 1.2 x 10^2 m away and runner b will be 1.3 x 10^2 m away from the starting point. runner a will be 72 x 10^3 m away and runner b will be 59.5 x 10^3 m away from the starting point. runner a will be 1.2 x 10^2 m away and runner b will be 1.1 x 10^2 m away from the starting point. runner a will be 7.2 x 10^2 m away and runner b will be 1.3 x 10^2 m away from the starting point.

Explanation:

Step1: Find Runner A's speed

Speed = distance / time. Runner A takes 25 s to go 64 m.
$v_A = \frac{64}{25} = 2.56$ m/s

Step2: Find Runner B's speed

Runner B starts 2.5 s late, so time taken is $25 - 2.5 = 22.5$ s to go 64 m.
$v_B = \frac{64}{22.5} \approx 2.844$ m/s

Step3: Calculate Runner A's distance at 45 s

Distance = speed × time.
$d_A = 2.56 \times 45 = 115.2 \approx 1.2 \times 10^2$ m

Step4: Calculate Runner B's distance at 45 s

Runner B's running time is $45 - 2.5 = 42.5$ s.
$d_B = 2.844 \times 42.5 \approx 120.87 \approx 1.3 \times 10^2$ m

Answer:

Runner A will be 1.2 x 10^2 m away and Runner B will be 1.3 x 10^2 m away from the starting point.