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Colton is taking a long bike ride where he rides at a constant speed. The distance he bikes is proportional to the amount of time he has been biking. After 3.5 hours, he has traveled a distance of 49 miles.(b) Colton travels at the same rate as in (a) for 6 hours. Let d be the distance he biked. Set up and solve a proportion for d. (c) Colton would like to bike 200 miles. Let h be the number of hours it will take Colton to bike this distance. Solve a proportion for h. Round to the nearest tenth of an hour.

Sagot :

isyllus

Answer:

b) [tex]d[/tex] = 84 miles

c) [tex]h[/tex] = 14.3 hours

Step-by-step explanation:

Given that:

The speed of Colton is constant while riding a bike.

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

If speed is constant, then we can deduct that:

[tex]Distance \propto Time[/tex]

Time = 3.5 hours

Distance = 49 miles

Therefore, the speed will be equal to:

Speed = [tex]\frac{49}{3.5}[/tex] = 14 miles/hr

b) Given that:

Time = 6 hours, then we have to find the distance to be hiked if the speed is same.

[tex]14 = \dfrac{d}{6}\\\Rightarrow d = \bold{84}\ miles/hr[/tex]

c) Given that:

Distance = 200 miles

Number of hours = [tex]h[/tex]

To find, the value of [tex]h[/tex].

[tex]14 = \dfrac{200}{h}\\\Rightarrow h = \dfrac{200}{14}\\\Rightarrow h = \bold{14.3}\ hours[/tex]

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