Question

In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length, in metres, of the racecourse?

• A. 880
• B. 990
• C. 770
• D. 660

Answer 1

The Correct Option is A

Let the first, second, and third horses be A, B, and C respectively. Let the total length of the racecourse be denoted as x.

From the first condition:
When A finishes the race (i.e., covers distance x), B is 11 meters behind and C is 90 meters behind. That means:

• B has covered: \( x - 11 \)
• C has covered: \( x - 90 \)

From the second condition:
When B finishes the race (i.e., covers distance x), C is 80 meters behind, so:

• C has covered: \( x - 80 \)

Now we form a ratio equation from the first condition:

Since the ratio of the distances covered by C and B when A finishes is: \[ \frac{x - 90}{x - 11} \] and from the second condition, the distance C runs when B finishes is: \[ x - 80 \] and when A finishes, B has covered \( x - 11 \), so both cases reference B and C’s relative speeds, hence: \[ \frac{x - 90}{x - 80} = \frac{x - 11}{x} \]

Simplify the equation:

\[ (x - 90) \cdot x = (x - 80)(x - 11) \] \[ x^2 - 90x = x^2 - 91x + 880 \] \[ -90x = -91x + 880 \Rightarrow x = 880 \]

Answer: \( \boxed{x = 880} \)