SOLUTION: Every morning at precisely 6:00 am, Susie begins her jogging circuit of the neighborhood. It’s a hilly route with no level stretches. Her uphill speed is always 2 miles per hour an
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Question 875011: Every morning at precisely 6:00 am, Susie begins her jogging circuit of the neighborhood. It’s a hilly route with no level stretches. Her uphill speed is always 2 miles per hour and her downhill speed is always 6 miles per hour. Ordinarily she completes her circuit at 7:00 am, but yesterday she completed it at 8:00 am. The only difference is that she ran the course counterclockwise rather than clockwise. How long is the course (in miles)? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Every morning at precisely 6:00 am, Susie begins her jogging circuit of the neighborhood.
It’s a hilly route with no level stretches.
Her uphill speed is always 2 miles per hour and her downhill speed is always 6 miles per hour.
Ordinarily she completes her circuit at 7:00 am, but yesterday she completed it at 8:00 am.
The only difference is that she ran the course counterclockwise rather than clockwise.
How long is the course (in miles)?
:
Let x = original up-hill distance, at 2 mph
Let y = original down-hill distance, at 6 mph
:
When he reverses the the circuit (goes counterclockwise)
x = down-hill distance, at 6 mph
y = up-hill distance, at 2 mph
:
Write a time equation for each circuit, time = dist/speed + = 1 hr + = 2 hr
:
multiply both equations by 6 to clear the denominators
3x + y = 6
x + 3y = 12
:
Multiply the 1st equation by 3, subtract the 2nd equation
9x + 3y = 18
x + 3y = 12
---------------Subtraction eliminates y find x
8x = 6
x = 6/8 = .75 mi
:
Find y
.75 + 3y = 12
3y = 12 - .75
3y = 11.25
y = 11.25/3
y = 3.75
:
Find the distance of one circuit
.75 + 3.75 = 4.5 mi is the length of the course
