Find walking speed . Formula: Distance = rate* time

Question

Melissa walks 3 miles to the house of a friend and returns home on a bike. She averages 4 miles per hour faster when cycling than when walking and the total time for both trips is two hours. Find her walking speed 

Answer 1

we know that distance = rate x time

 

walking, the distance is 3 mi, and we can say that her rate is x miles , and the time it takes to walk is t hours

 

cycling, the distance is still 3 mi, but now her speed is (x + 4), and the time it takes is (2 - t) hours

 

Now, let's substitute into our formula for the distance.

 

Equation 1 is 3 = xt

 

Equation 2 is 3 = (x + 4)(2 - t)

 

We can solve the first equation for t

 

t = 3/x

 

Now, plug this value of t into the second equation

 

3 = (x + 4)(2 - 3/x)

 

3 = 2x - 3 + 8 - 12/x

 

3 = 2x + 5 - 12/x

 

3x = 2x² + 5x - 12

 

2x² + 2x - 12 = 0

 

x² + x - 6 = 0

 

(x - 2)(x + 3) = 0

 

x = 2 and x = -3

 

The only logical solution is x = 2 because x cannot be negative

 

Therefore, Melissa's walking speed is 2 mph