At what speed was the jogger going?

Question

A woman jogged to a park, she ran 7 miles. She took a different route home that was 14 miles. The route home took her an hour longer. If she jogged at the same pace to and from, at what speed was she moving?

Answer 1

Hi Nicole, use the D(istance) = R(ate) * T(ime) equation. 

 

Given: the rate is the same going from and returning home.

 

Given: the time going from home can be represented by h. The time returning home is then represented by (h + 1).

 

Given: Distance going from home equals 7 miles. Distance returning home equals 14 miles.

 

Missing: Rate, but the rate is constant both going from home and returning home.

 

Equation, going from home:

 

d = r_g * t

 

Substituting:

 

7 = r_g * h

 

Solve for r_g:

 

r_g = 7 / h

 

Equation returning home:

 

d = r_r * t

 

Substituting:

 

14 = r _r* (h + 1)

 

Solve for r_r:

 

r_r = 14 / (h + 1)

 

Since the rate is constant:

 

r_g = r_r

 

Substitute for rates:

 

7 / h = 14 / (h + 1)

 

Cross-multiply:

 

7 * (h + 1) + 14 * h

 

Solve for h:

 

7h + 7 = 14h

 

h = 1

 

We know know how much time the jogger spent going from home and returning home, 1 hour. We can now find the rate:

 

d = r * t

 

Substituting:

 

d = 7

 

t = 1

 

Solve for r

 

7 = r * 1

 

r = 7

 

The woman's rate was 7 mph.

 

Questions?