A woman rides her bicycle from her house to and from a lake. It takes her 1 1/2 hours to ride to the lake and 1 3/4 hours to ride back. She rides downhill at 12 kilometers per hour, on level ground at 8 kilometers per hour, and uphill at 6 kilometers per hour. What is the distance in kilometers from her house to the lake?

Question

A woman rides her bicycle from her house to and from a lake. It takes her 1 1/2 hours to ride to the lake and 1 3/4 hours to ride back. She rides downhill at 12 kilometers per hour, on level ground at 8 kilometers per hour, and uphill at 6 kilometers per hour. What is the distance in kilometers from her house to the lake?

Answer 1

To find the distance from her house to the lake, we can use the formula:

Distance = Time × Speed

Let's break down the journey into different sections: downhill, level ground, and uphill.

1. Downhill:
The woman rides downhill at a speed of 12 kilometers per hour. The time it takes her to ride downhill is 1 1/2 hours. So the distance she covers downhill can be calculated as:
Distance_downhill = Time_downhill × Speed_downhill
Distance_downhill = 1 1/2 hours × 12 kilometers per hour

We need to convert the time to a fraction of an hour for calculation purposes. 1 1/2 hours is equal to 1.5 hours.

Distance_downhill = 1.5 hours × 12 kilometers per hour

2. Level Ground:
The woman rides on level ground at a speed of 8 kilometers per hour. The time it takes her to ride on level ground is not given explicitly, but we know that the total round trip took 1 3/4 hours. Since the downhill and uphill durations are given, we can calculate the time spent on level ground:
Time_level_ground = Total_time - Time_downhill - Time_uphill

To calculate Time_level_ground, first convert the total time to a fraction of an hour:
Total_time = 1 3/4 hours = 1.75 hours

Then subtract the time for downhill and uphill:
Time_level_ground = 1.75 hours - 1.5 hours - 1.75 hours

3. Uphill:
The woman rides uphill at a speed of 6 kilometers per hour. The time it takes her to ride uphill is 1 3/4 hours. Using the same process as before, we can calculate the distance covered uphill:
Distance_uphill = Time_uphill × Speed_uphill
Distance_uphill = 1.75 hours × 6 kilometers per hour

Now that we have the distances for each section, we can find the total distance from her house to the lake by adding up the distances for each section:
Total_distance = Distance_downhill + Distance_level_ground + Distance_uphill

Substituting the values we calculated earlier:
Total_distance = (1.5 hours × 12 kilometers per hour) + (Time_level_ground × 8 kilometers per hour) + (1.75 hours × 6 kilometers per hour)

Now we can evaluate this expression to find the total distance from her house to the lake.