Question

Ari is swimming a 25-meter race. After swimming 6 meters, she catches up to Amanda in a ratio of 7:3 from the 6-meter mark. At what meter mark does Ari catch up to Amanda? Round to the nearest tenth, if necessary.

Ari catches up to Amanda at _______ meters.

Answer 1

Answer:

Ari catches up to Amanda at 19.3 meters

Step-by-step explanation:

Given :

Ari is swimming a 25-meter race.

After swimming 6 meters she catches up to Amanda in a ratio of 7:3 from the 6-meter mark.

Solution :

The distance between 6 meters and 25 meters = 19 meters.

Since she catched Amanda in ratio 7:3

So, she catched her at 7/10 of the distance

So, the distance at which she catched Amanda = $\frac{7}{10} *19$

                                                                               =13.3

Ari catches 13.3 metres from 6 m marks

The point on number line at which she catches her = 13.3+6

Hence Ari catches up to Amanda at 19.3 meters

Answer 2

The position where Ari caught up with Amanda using the ratio principle is 19.3 meters

• The total distance = 25 meters

• Distance left after catching up = 25 - 6 = 19 meters

• Ratio = 7 : 3

Ari's position when she catches up with Amanda :

• (Ari's ratio ÷ sum of ratio) × distance

Ari's position = (7÷10) × 19 = 13.3

Therefore, Ari caught up with Amanda at the point 13.3 meters mark

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