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Stanley runs, swims, and bikes every day. During these workouts, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
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What distance did Stanley cover while biking?

Respuesta :

The time spent for each activity can be found writing an equation based on

the known parameters.

  • The duration of the time Stanley spent running is 1.5 hours
  • The duration of the time Stanley spent swimming is 1 hour
  • The duration of the time Stanley spent Biking is 3 hours

  • The distance Stanley cover while biking is 48 miles

Reasons:

The running speed = 9 mph

The biking speed = 16 mph

Swimming speed = 2.5 mph

The time spent running = 0.5 hour + Time spent swimming

Biking time = 2 × Running time

The total distance covered = 64 miles

Required:

Time spent running, swimming, and biking

Solution:

Let t represent the time Stanley spent swimming, we have;

(t + 0.5)·9 + 2.5·t + 2×(t + 0.5)×16 = 64

43.5·t + 20.5 = 64

43.5·t  = 64 - 20.5 = 43.5

[tex]t = \dfrac{43.5}{43.5} = 1[/tex]

  • The time Stanley spent swimming, t = 1 hour

The time Stanley spent running = 0.5 + t

Therefore;

The time spent running = 0.5 hour + 1 hour = 1.5 hour

  • Time spent running = 1.5 hours

Time spent biking = 2 × Running time

Therefore;

  • Time spent biking = 2 × 1.5 hours = 3 hours

  • The distance Stanley cover while biking, d = 3 × 16 mph = 48 miles

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