in a race A beats B by 100m. the ratio of their speeds is 5:4 . what is the length of the racecourse?
600m
500m
30
Why did A beat B in the race? Because A is a fast runner, but B is just a slow-poke! Now, let's calculate the length of the racecourse.
If A beat B by 100m, it means in the time it takes B to run the entire race, A managed to run 100m more.
So, let's set up some equations. Let's say A's speed is 5x, and B's speed is 4x (since the ratio of their speeds is 5:4).
In the time it takes B to run the racecourse, A would have run the racecourse plus an extra 100m.
So, we can set up the equation:
5x * (time taken by B) = 4x * (time taken by B) + 100m
Simplifying the equation, we have:
5x * (time taken by B) - 4x * (time taken by B) = 100m
x * (time taken by B) = 100m
Since the time taken by B cancels out, we're left with x = 100m.
Since x represents the length of 1 unit in the ratio of their speeds, the total length of the racecourse would be:
5x + 100m = 5 * 100m + 100m = 500m + 100m = 600m
So, the length of the racecourse is 600m.
And remember, in a race, it's not just about the length of the course, it's also about the spirit of competition and the joy of running! Keep running, my friend!
To find the length of the racecourse, we need to determine the speed at which both A and B are running.
Given that A beats B by 100m, we can say that when A finishes the race, B is 100m behind. Let's assume that A takes time 't' to finish the race, while B takes time 't + x' to finish the race, where 'x' is the extra time B takes to finish after A.
Now, we know that the ratio of their speeds is 5:4. Let's assume the speed of A is 5v and the speed of B is 4v, where 'v' is a common factor.
Since distance = speed × time, we can write the following equations:
Distance covered by A = speed of A × time taken by A = 5v × t
Distance covered by B = speed of B × time taken by B = 4v × (t + x)
Given that A beats B by 100m, we have:
Distance covered by A - Distance covered by B = 100m
Substituting the above distances, we have:
5v × t - 4v × (t + x) = 100m
Simplifying the equation:
5vt - 4vt - 4vx = 100m
vt - 4vx = 100m
t - 4x = 100m
Now, we need to find another equation to solve for 'x'. Since we already know that A beats B by 100m, we can equate the distance covered by A and B:
5v × t = 4v × (t + x)
Simplifying the equation:
5vt = 4vt + 4vx
5vt - 4vt = 4vx
vt = 4vx
Now, we can substitute the value of vt in the equation t - 4x = 100m:
4vx - 4x = 100m
4x(v - 1) = 100m
x(v - 1) = 25m
To solve for 'x' and 'v', we need another equation. Let's use the fact that the ratio of their speeds is 5:4:
5v/4v = 5/4
Cross-multiplying:
5v × 4 = 4v × 5
20v = 20v
Since both sides are equal, we can conclude that the above equation is satisfied regardless of the value of 'v'. Therefore, 'v' can take any positive value.
Now, let's solve for 'x':
x(v - 1) = 25m
Since 'v' can be any positive value, let's take an example where 'v' is 1:
x(1 - 1) = 25m
0 = 25m
We can see that this equation will not hold true for any valid value of 'x'. Therefore, there is no solution for the given information.
Hence, without any additional information or constraints, we cannot determine the length of the racecourse.