Question

Pls help :)

Angie is really fit and wants to test her endurance by competing in a swimming competition over four days. On the first day, she covers 25 per cent of the distance. On the second day, she covers one third of the remaining distance, on the third day, 25 per cent of the remaining distance and, on the final day, she swims half of the remaining distance. She still has 15km to swim to complete the competition. Form a linear equation and find the total distance of the swimming competition. (Use x as the total distance of the swimming competition).

Answer 1

Answer: Total distance of the swimming competition is 55.56 km.

Explanation:

Let x be the total distance of the swimming competition.

On the first day, Angie covered 25% of the total distance, which means she swam 0.25x km.

On the second day, she covered one-third of the remaining distance, which is (1 - 0.25)x = 0.75x km.

So, she swam (1/3) * 0.75x = 0.25x km on the second day.

On the third day, she covered 25% of the remaining distance, which is (1 - 0.25 - 1/3)x = 0.42x km.

So, she swam 0.25 * 0.42x = 0.105x km on the third day.

On the final day, she swam half of the remaining distance,

which is (1 - 0.25 - 1/3 - 0.5)x = 0.125x km.

The total distance she swam is the sum of the distances swum on each day:

0.25x + 0.25x + 0.105x + 0.125x = 0.73x

We know that the total distance of the competition is x - 15 km (since she still has 15 km left to swim).

So we can set up the equation:

0.73x = x - 15

Solving for x, we get:

x-0.73x = 15

0.27x = 15

x = 55.56

Therefore, the total distance of the swimming competition is 55.56 km.

Answer 2

Let's start by using algebra to represent the problem mathematically.

On the first day, Angie covers 25% of the total distance, which can be written as:

0.25x

On the second day, she covers one third of the remaining distance. After the first day, she has 75% of the total distance left to cover. So, the distance she covers on the second day can be written as:

(1/3)(0.75x) = 0.25x

On the third day, she covers 25% of the remaining distance. After the first two days, she has 50% of the total distance left to cover. So, the distance she covers on the third day can be written as:

0.25(0.5x) = 0.125x

On the final day, she covers half of the remaining distance. After the first three days, she has 25% of the total distance left to cover. So, the distance she covers on the final day can be written as:

0.5(0.25x) = 0.125x

Adding up the distances she covered on each day, we get:

0.25x + 0.25x + 0.125x + 0.125x = 0.75x

This represents the total distance she covered over the four days.

We know that Angie still has 15km left to swim to complete the competition. So, we can set the total distance x equal to the distance she covered plus the remaining distance:

0.75x + 15 = x

Solving for x, we get:

0.25x = 15

x = 60

Therefore, the total distance of the swimming competition is 60km.