Alexandra and Chi compete in an Olympic-type triathlon consisting of a 1.5 km swim, a 40 km bicycle ride, and a 10 km run. There are two transitions in the race where the participants take time to change from one mode of the race to another. Their times from the race are shown. Complete questions 1dash4 below. Alexandra

Chi

Swim

5 km/hr

6 km/hr

Transition 1

4 minutes

5 minutes

Cycle

15 km/hr

15 km/hr

Transition 2

3 minutes

5 minutes

Run

6 km/hr

7.5 km/hr

Complete question :

Alexandra and Chi compete in an Olympic-type triathlon consisting of a 1.5 km swim, a 40 km bicycle ride, and a 10 km run. There are two transitions in the race where the participants take time to change from one mode of the race to another. Their times from the race are shown. Complete questions 1dash4 below.

How long does it take Alexandra to complete the triathlon. Write a linear equation to model total time t in hours.

Kindly check explanation

Step-by-step explanation:

Given the following :

SWIM:

Alexandra __5km/hr

Chi 6km/hr

Transition 1:

Alexandra __ 4 minutes

Chi 5 minutes

CYCLE:

Alexandra __15km/hr

Chi 15km/hr

Transition 2:

Alexandra __ 3 minutes

Chi 5 minutes

RUN:

Alexandra __6km/hr

Chi 7.5km/hr

Distances:

swim distance = 1.5km

bicycle ride distance = 40km

run distance = 10km

Time taken by Alexandra :

time = distance / speed

Swim time = 1.5km / 5km/hr = 0.3 hr

Transition 1 = 4/60 = 0.067 hr

Cycle time = 40km / 15km/hr = 2.67 hours

Transition 2 = 3/60 = 0.05 hr

Run time = 10 / 6km/hr = 1.67 hrs

Total time(t) in hours taken by Alexandra :

(0.3 + 0.067 + 2.67 + 0.05 + 1.67) hrs = 4.757 hours

Time taken by Chi :

time = distance / speed

Swim time = 1.5km / 6km/hr = 0.25 hr

Transition 1 = 5/60 = 0.083 hr

Cycle time = 40km / 15km/hr = 2.67 hours

Transition 2 = 5/60 = 0.083 hr

Run time = 10 / 7.5km/hr = 1.33 hrs

Total time(t) in hours taken by Chi

(0.25 + 0.083 + 2.67 + 0.083 + 1.33) hrs = 4.757 hours = 4.416 hours

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.