In a 10 km race, A, B and C each run at uniform speed, get the first, second and third position respectively. If A beats B by 1 km and B beats C by 1 km, then, by how much distance A beat C?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.9 km
Let the speeds of A, B, C be $v_A, v_B, v_C$ respectively.
Race distance = 10 km
A beats B by 1 km → when A runs 10 km, B runs 9 km:
$\frac{v_B}{v_A} = \frac{9}{10}$
B beats C by 1 km → when B runs 10 km, C runs 9 km:
$\frac{v_C}{v_B} = \frac{9}{10} \Rightarrow v_C = \frac{9}{10} v_B = \frac{9}{10} \cdot \frac{9}{10} v_A = \frac{81}{100} v_A$
Distance C runs when A runs 10 km:
$d_C = v_C \cdot \frac{10}{v_A} = \frac{81}{100} v_A \cdot \frac{10}{v_A} = 8.1 \text{ km}$
A beats C by: $10 - 8.1 = 1.9$ km