SOLUTION: suppose you can run 250meters per minute downhill and 180 meters per minute uphill. One day you run 1557 meters in 7.6 minutes always either uphill or downhill. Solve the linear sy

Question 261738: suppose you can run 250meters per minute downhill and 180 meters per minute uphill. One day you run 1557 meters in 7.6 minutes always either uphill or downhill. Solve the linear system to find the number of meters you ran uphill and downhill.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate downhill = 250 meters per minute.
rate uphill = 180 meters per minute.
total distance = 1557 meters.
total time is 7.6 minutes.

x = number of minutes downhill.
y = number of minutes uphill.

x + y = 7.6

rate * time = distance

250*x + 180*y = 1557

solve these 2 equations simultaneously.

solve for y in first equation to get y = 7.6 - x

substitute for y in second equation to get 250*x + 180*(7.6-x) = 1557

simplify second equation to get:

250*x + 180*7.6 - 180*x = 1557

simplify further and combine like terms to get:

70*x + 1368 = 1557

subtract 1368 from both sides of equation to get:

70*x = 1557 - 1368 = 189

divide both sides of equation by 70 to get:

x = 189/70 = 2.7

y = 7.6 - x becomes 7.6 - 2.7 = 4.9

you have x = 2.7 minutes downhill and y = 4.9 minutes uphill.

first equation of x + y = 7.6 becomes 2.7 + 4.9 = 7.6 becomes 7.6 = 7.6 confirming values for x and y are good for first equation.

second equation of 250*x + 180*y = 1557 becomes 250*2.7 + 180*4.9 = 1557 becomes 675 + 882 = 1557 becomes 1557 = 1557 confirming values for x and y are good for second equation.

your answer is:

he ran 675 meters downhill and 882 meters uphill.

this is because:

rate * time = distance

250*2.7 = 675 meters downhill.

180*4.9 = 882 meters uphill.

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