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Katen [24]
3 years ago
12

Devontre rode his bike uphill 5 miles and then back downhill. The rate at which Devontre traveled downhill was 20 mph faster tha

n his rate going uphill. If it took him 20 minutes longer to ride uphill than downhill, what was his uphill rate?
Mathematics
1 answer:
Daniel [21]3 years ago
5 0

Answer:

10 mph

Step-by-step explanation:

Let x mph be Devontre rate uphill, then x+20 mph its his rate downhill.

1. Time uphill:

\dfrac{5}{x}\ hours

2. Time downhill:

\dfrac{5}{x+20}\ hours

3. If it took him 20 minutes (1/3 hour) longer to ride uphill than downhill, then

\dfrac{5}{x}-\dfrac{5}{x+20}=\dfrac{1}{3}

Solve this equation:

\dfrac{5(x+20)-5x}{x(x+20)}=\dfrac{1}{3}\\ \\\dfrac{100}{x(x+20)}=\dfrac{1}{3}\\ \\300=x(x+20)\\ \\x^2+20x-300=0\\ \\D=20^2-4\cdot (-300)=400+1200=1600\\ \\x_{1,2}=\dfrac{-20\pm \sqrt{1600}}{2}=\dfrac{-20\pm 40}{2}=-30,\ 10.

The rate cannot be negative, thus, x=10 mph (rate uphill).

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2 years ago
A golfer takes two putts to get the ball into the hole. The first putt rolls the ball 10.3 feet in the northwest direction and t
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Let's put this on the usual Cartesian grid just so we can talk about it without drawing a picture.  We'll use map conventions, right is east, up is north.

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The sides of these triangles are in ratio 1:1:\sqrt{2} so the coordinates after the first putt are

(- 10.3 / \sqrt{2}, 10.3 / \sqrt{2})

The negative sign indicates west, which doesn't really matter for this problem.  The distance from the origin to this point is 10.3 as required.

Now a second putt of 3.8 feet north puts us at
 
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