Question 1036540
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Hello, I need help with a question for homework for Algebra.

"Melissa walks 3km to the house of a friend and returns home on a bike. She averages 4km per hour faster when cycling than when walking, 
and the total time for both trips is two hours/ Find her walking speed, given that the formula for calculating time (in hours) is:  t=d/s
where d=distance (in km)
and s=speed (in km/h)"

I know that the walking speed is 1km/h but I cannot understand how to show the working algebraically.

If you could help I would be very grateful.

Kind Regards

Benjamin Austin
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<pre>
Let u be Melissa's walking speed, in {{{km/h}}}.

Then her biking speed is (u+4) {{{km/h}}}.

The equation is

{{{3/x}}} + {{{3/(x+4)}}} = 2

To solve it, multiply both sides by x*(x+4) to rid of denominators.

You will get a quadratic equation. Simplify and solve.

3(x+4) + 3x = 2x*(x+4),

6x + 4 = {{{2x^2 + 8x}}},

{{{2x^2 -2x + 4}}} = {{{0}}},

{{{x^2 - x + 2}}} = {{{0}}},

Factor left side

(x-2)*(x+1) = 0.

One root is x = -1. Disregard it as negative.

The other root is x = 2 {{km/h}}}.

Check if it is correct.

<U>Answer</U>. Melissa's walking speed is 2 {{{km/h}}}. Her biking speed is 6 {{{km/h}}}.
</pre>