Without taking a single break, mercedes hiked for 10 hours, up a mountain and back down by the same path. While hiking, she averaged 2 miles per hour on the way up and 3 miles per hour on the way down. How many miles was it from the base of the mountain to the top?
time = distance/speed.
add up the times:
d/2 + d/3 = 10
d = 12
To find the distance from the base of the mountain to the top, we need to calculate the total distance traveled while hiking uphill and downhill separately, and then add them together.
Let's start with the uphill portion:
Given that Mercedes hiked for 10 hours and averaged 2 miles per hour, we can multiply the average speed by the time to find the distance traveled uphill:
Distance uphill = Average speed uphill × Time hiking uphill
Distance uphill = 2 miles/hour × 10 hours
Distance uphill = 20 miles
Now let's calculate the distance for the downhill portion:
Given that Mercedes hiked for 10 hours and averaged 3 miles per hour downhill, we can use the same formula to find the distance traveled downhill:
Distance downhill = Average speed downhill × Time hiking downhill
Distance downhill = 3 miles/hour × 10 hours
Distance downhill = 30 miles
Since Mercedes hiked up and down the same path, the distance from the base of the mountain to the top is equal to the distance traveled uphill. Therefore, the distance from the base to the top is 20 miles.