'A' can run 1 km in 5 minutes 20 seconds and 'B' can run the same distance in 6 minutes. How many meters start can 'A' give 'B' in a kilometer race so that they finish the race together?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 111.1 meter **
Speed of A:
$5$ minutes $20$ seconds $= 320$ seconds
$\text{Speed}_A=\frac{1000}{320}=\frac{25}{8}$ m/s
Speed of B:
$6$ minutes $= 360$ seconds
$\text{Speed}_B=\frac{1000}{360}=\frac{25}{9}$ m/s
Let the head start given to B be $d$ meters. Then A runs $1000$ m while B runs $(1000-d)$ m in the same time.
Time equality:
$\frac{1000}{\frac{25}{8}}=\frac{1000-d}{\frac{25}{9}}$
Simplify:
$1000 \cdot \frac{8}{25} = (1000-d)\cdot \frac{9}{25}$
$320 = \frac{9(1000-d)}{25}$
$8000 = 9(1000-d)$
$8000 = 9000 - 9d$
$9d = 1000$
$d = \frac{1000}{9} \approx 111.11$
A can give B a start of $\frac{1000}{9}$ meters (≈ 111.11 m).