jenniferracer10
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Suppose you have entered 79​-mile biathlon that consists of a run and a bicycle race. During your​ run, your average velocity is miles 5per​ hour, and during your bicycle​ race, your average velocity is 23 miles per hour. You finish the race in 5 hours. What is the distance of the​ run? What is the distance of the bicycle​ race?

Sagot :

chetankachana

Answer:

The distance of the run is 10 miles

The distance of the bicycle race is 69 miles

Step-by-step explanation:

Let:

  • r = the distance for the run
  • 79 - r = the distance for the bicycle race
  • t = the time of the run
  • 5 - t = the time of the bicycle race

The run: r = 5t

The bicycle race: 79 - r = 23(5 - t)

Simplify the bicycle race:

  • 79 - r = 115 - 23t
  • -r = 36 - 23t
  • r = 23t - 36

Now we have two equations set up for r

  • r = 5t
  • r = 23t - 36

We know that r = r, so 5t must equal 23t - 36

  • 5t = 23t - 36
  • 5t + 36 = 23t
  • 36 = 18t
  • t = 2

Now we know that the run took 2 hours.

Plug it back into the equation for the run to find the distance for the run

  • r = 5t
  • r = 5(2)
  • r = 10

The run is 10 miles

To solve for the bicycle race, we simply subtract 10 from 79, because we know that the two distances combined are 79.

  • 79 - 10 = 69

The bicycle race is 69 miles.

-Chetan K

sqdancefan

Answer:

  • run: 10 miles
  • bike race: 69 miles

Step-by-step explanation:

Let r represent the distance run. Then 79-r is the distance biked. The total time is ...

  time = distance/speed

  5 = (r/5) +(79-r)/23 . . . . sum of time running and time biking

  575 = 23r +5(79 -r) . . . . multiply by 115

  180 = 18r . . . . . . . . . . . . . subtract 395

  10 = r . . . . . . . . . . . divide by 18

  79-r = 69 . . . . . . distance biking

The distance of the run is 10 miles; the bicycle race is 69 miles.

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