Monday, October 04, 2004
How long Grass Last?
It is known that if 10 sheep are turned out in the field, the grass will be gone in 20 days. On the other hand, if 15 sheep are turned out in the field, the grass will be gone in 10 days. If 25 sheep are turned out in the field, when will the grass be gone?
Answer:
Let r is the unit of grass grown per day. Let g be the total units of grass in the field before the sheep are turned out. Let s be the number of units of grass each sheep eats perday. We must determine the constant values of g and r from the information given in the problem. The total number of grass units eaten equals the number of days times the amount of grass the sheep eat per day. From this, we can construct two equations: g + 20r = 20(10s). g + 10r = 10(15s)Reducing the equations, we obtain: g + 20r = 200s. g + 10r = 150s. Subtract one equation from the other: 10r = 50 s. So r equals 5s. Substituting back, we discover g equals 100s. Now we construct an equation for the case of having 25 sheep turned out inthe field, where x is the number of days it takes the sheep to eat all the grass: g + xr = x(25s). 100s + x(5s) = x(25s) 20sx =100s. x = 5. So 25 sheep would consume all the grass in the field in 5 days.
Answer:
Let r is the unit of grass grown per day. Let g be the total units of grass in the field before the sheep are turned out. Let s be the number of units of grass each sheep eats perday. We must determine the constant values of g and r from the information given in the problem. The total number of grass units eaten equals the number of days times the amount of grass the sheep eat per day. From this, we can construct two equations: g + 20r = 20(10s). g + 10r = 10(15s)Reducing the equations, we obtain: g + 20r = 200s. g + 10r = 150s. Subtract one equation from the other: 10r = 50 s. So r equals 5s. Substituting back, we discover g equals 100s. Now we construct an equation for the case of having 25 sheep turned out inthe field, where x is the number of days it takes the sheep to eat all the grass: g + xr = x(25s). 100s + x(5s) = x(25s) 20sx =100s. x = 5. So 25 sheep would consume all the grass in the field in 5 days.
# posted by padmaram @ 11:25 AM 
