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Jim began a ​189-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 6 hours. If Jim walks at a rate of 4 miles per hour and rides at 34 miles per​ hour, find the amount of time he spent on the bicycle.

Jim rode for _ hours.

Respuesta :

MrRoyal

Jim rode for 5.5 hours

The given parameters are:

[tex]Distance = 189miles[/tex] -- the total distance

[tex]Time= 6hours[/tex] --- the total time

The rates are given as:

[tex]w = 4mi/hr[/tex] ---- walks

[tex]r = 34mi/hr[/tex] --- ride

So, we have the following equation

[tex]t_w + t_r = 6[/tex] --- the sum of time walking and riding the bicycle

[tex]d_w + d_r = 189[/tex] --- the sum of distance walked and riding the bicycle

Make dr and tr the subjects in the above equations

[tex]t_r = 6 - t_w[/tex]

[tex]d_r = 189 - d_w[/tex]

The equation for distance walked is:

[tex]w = \frac{d}{t}[/tex]

So, we have:

[tex]4 = \frac{d}{t}[/tex]

Make d the subject

[tex]d = 4t[/tex]

Rewrite as:

[tex]d_w = 4t_w[/tex]

For riding the bicycle, we have:

[tex]r = \frac{d}{t}[/tex]

So, we have:

[tex]34 = \frac{189 - d_w}{6 -t_w}[/tex]

Open brackets

[tex]204 - 34t_w = 189 - d_w[/tex]

Rewrite as:

[tex]d_w =34t_w + 189 - 204[/tex]

[tex]d_w =34t_w-15[/tex]

Substitute [tex]d_w =34t_w-15[/tex] in [tex]d_w = 4t_w[/tex]

[tex]34t_w - 15 = 4t_w[/tex]

Collect like terms

[tex]34t_w - 4t_w = 15[/tex]

[tex]30t_w = 15[/tex]

Divide both sides by 30

[tex]t_w = 0.5[/tex]

Recall that:

[tex]t_r = 6 - t_w[/tex]

So, we have:

[tex]t_r = 6 - 0.5[/tex]

[tex]t_r = 5.5[/tex]

Hence, Jim rode for 5.5 hours

Read more about speed and distance at:

https://brainly.com/question/2854969