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Algebra : Word Problems and Systems of Equations

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Rowing Speed:
Hank can row a boat 1 mi upstream (against the current) in 24 min. He can row the same distance downstream in 13min. If both the rowing speed and current speed are constant, find Hank's rowing speed and the speed of the current.

Airplane Speed - An airplane flying with the wind from Los Angeles to New York City takes 3.75 hr. Flying against the wind, the airplane takes 4.4 hr. for the return trip. If the air distance between Los Angeles and New York is 2500 mi and the airplane speed and wind speed are constant, find the airplane speed and the wind speed.

Food Prices: At Philip's convenience store the total cost of one medium and one large soda is $1.74. The large soda costs $.016 more than the medium soda. Find the cost of each soda.

Nut Mixture
A 5lb. nut mixture is worth $2.80 per pound. The mixture contains peanuts worth $1.70 per pound and cashews worth $4.55 per pound. How many pounds of each type of nut are in the mixture?

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Word problems are solved using systems of equations. The solution is detailed and well presented.

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1. Rowing Speed:
Hank can row a boat 1 mi upstream (against the current) in 24 min. He can row the same distance downstream in 13min. If both the rowing speed and current speed are constant, find Hank's rowing speed and the speed of the current.

Rowing speed: x miles per min
Speed of current: y miles per min
In the upstream, his actual speed is (x - y) miles per min
In the downstream, his actual speed is (x + y) miles per min
Speed = Distance / time
In upstream, (1)
In downstream, (2)
Solving the linear system (1) and (2):
(1) + (2)
(2) - (1)
...

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