Marlene rides her bicycle to her friend jon's house and returns home by the same route. marlene rides her bike at constant speeds of 9 mph on level ground, 6 mph when going uphill and 18 mph when going downhill. if her total time riding was 1 hours, how far is it to jon's house?

To solve the problem:

Let f = distance one way distance on level ground

Let h = distance rode on the hill

Write a time equation; where Time = distance/speed:

level time + uphill time + downhill time + level time = 1hr

f/9 + h/6 + h/18 + f/9 = 1 hr

Multiply equation by 18 to get rid of the denominators

2f + 3h + h + 2f = 18

4f + 4h = 18

Simplify by dividing this by 4

f + h = 4.5 miles is took her to get to Jon’s house.