The diagram (Triangle ABC) shows 3 sections of a level triathlon course. In order to complete the triathlon, each contestant must swim 4 km from C to B, cycle from B to A, and then run 28 km from A to C. Mary can cycle at an average speed of 25 km/hour. It takes her 1 hour and 12 minutes to cycle from B to A. (a) Show that the total length of the course is 62 km. (b) On average, Mary can run 5-6 times as fast as she can swim. It takes her 4.8 hours to complete the course. Find her average swimming speed in km/h.

Leaving Cert Mathematics Algebra: The diagram (Triangle ABC) shows

The diagram (Triangle ABC) shows 3 sections of a level triathlon course - Leaving Cert Mathematics - Question 7 - 2021

Question 7

The diagram (Triangle ABC) shows 3 sections of a level triathlon course. In order to complete the triathlon, each contestant must swim 4 km from C to B, cycle from B... show full transcript

Worked Solution & Example Answer:The diagram (Triangle ABC) shows 3 sections of a level triathlon course - Leaving Cert Mathematics - Question 7 - 2021

Step 1

Show that the total length of the course is 62 km.

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Answer

To find the total length of the course, we need to consider each segment of the course:

Swimming from C to B: This is a fixed distance of 4 km.
Cycling from B to A:
- Mary cycles at an average speed of 25 km/h.
- The time taken to cycle from B to A is 1 hour and 12 minutes, which is equivalent to 1.2 hours.
- The distance for this segment can thus be calculated as: $ext{Distance} = ext{Speed} \times \text{Time} = 25 \text{ km/h} \times 1.2 \text{ h} = 30 \text{ km}$
Running from A to C: This segment has a given distance of 28 km.

Now, we can sum these distances:

$ext{Total Length} = 4 ext{ km} + 30 ext{ km} + 28 ext{ km} = 62 ext{ km}.$

Hence, the total length of the course is confirmed to be 62 km.

Step 2

Find her average swimming speed in km/h.

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Answer

To find Mary's average swimming speed, we first need to break down the total time taken to complete the course and how it relates to each segment:

Total Time for the Course: The total time taken is 4.8 hours.
Let x be the speed of swimming (in km/h).
Then, the time taken to swim is:
- $T_{swim} = \frac{4 \text{ km}}{x}$
The running distance (A to C) is 28 km, and if Mary runs at a speed of 5x (based on her swimming speed), the time taken to run is:
- $T_{run} = \frac{28 ext{ km}}{5x}$
The cycling time is known: 1.2 hours, so we have:

$T_{run} + T_{swim} + 1.2 = 4.8 \ ext{ hours}$

Substituting the equations:

$\frac{4}{x} + \frac{28}{5x} + 1.2 = 4.8$

This simplifies to:

$\frac{4 + 5.6}{x} + 1.2 = 4.8$

Thus,

$\frac{9.6}{x} + 1.2 = 4.8$

So,

$\frac{9.6}{x} = 3.6$

Solving for x:

$x = \frac{9.6}{3.6} = 2.67 \text{ km/h}.$

Therefore, Mary's average swimming speed is approximately 2.67 km/h.

The diagram (Triangle ABC) shows 3 sections of a level triathlon course - Leaving Cert Mathematics - Question 7 - 2021

Worked Solution & Example Answer:The diagram (Triangle ABC) shows 3 sections of a level triathlon course - Leaving Cert Mathematics - Question 7 - 2021

Show that the total length of the course is 62 km.

Find her average swimming speed in km/h.

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