A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and | MathCelebrity Forum

# A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and

#### math_celebrity

Staff member
A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.

Let Level distance = L and hill distance = H. Add the times it took for each section of the walk:
L/4 + H /3 + H/6 + L/4 = 5

The LCD of this is 12 from our LCD Calculator

Multiply each side through by our LCD of 12
3L + 4H + 2H + 3L = 60

Combine like terms:
6L + 6H = 60

Divide each side by 3:
2L + 2H = 20

The woman walked 20 miles