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Wewaii [24]
3 years ago
12

Surya is competing in a triathlon that includes swimming, bicycling and running. For the first two segments of the race, Surya s

wam at an average rate of 4 kilometers per hour and bicycled at an average rate of 40 kilometers per hour. It took 81.75 minutes for Surya to swim and cycle a combined total of 43.29 kilometers, completing the first two segments of the race. How long, in minutes, did it take him to complete the swimming portion of the race? Express your answer to the nearest hundredth.
If an athlete who completes this triathlon swims, bicycles and runs a combined total of 52.95 kilometers, the distance the athlete swam is what percent of the total race distance? Express your answer as a percent to the nearest hundredth.



At what average rate, in kilometers per hour, must Surya run the third, and final, portion of the race if he wishes to complete the entire race in no more than 140 minutes? Express your answer to the nearest hundredth
Mathematics
2 answers:
kirill115 [55]3 years ago
8 0
Hehshdndnzjxjbshzhsbsbsbsbzjzjn 29
jenyasd209 [6]3 years ago
8 0

Step-by-step explanation:

Let d_{1} be the distance Surya swam and d_{2} be the distance he bicycled. We know that   = 43.29 km.

Now let t_{1} and t_{2} be the time, in hours, it took Surya to complete the swimming and bicycling portions of  the race, respectively.

That means t_{1} + t_{2} = 81.75/60 = 1.3625 hours, and t_{2} = 1.3625 –  t_{1}

Using the  distance formula, we have d_{1} = 4t_{1} and d_{2} = 40t_{2}

= 40(1.3625 –t_{1} )

= 54.5 – 40 t_{1}

Substituting these  expressions for  and  in our first equation yields 4t_{1} + 54.5 – 40t_{1} = 43.29.

Solving for  we see that  - 36 t_{1}= - 11.21, meaning it took Surya t_{1} = 0.31138(Bar) hours to complete the swimming portion of the race.

This is equivalent to 0.31138(Bar)(60) = 18.683(Bar)≈ 18.68 minutes.

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