# Algebra : Word Problems and Systems of Equations

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?

https://brainmass.com/math/linear-algebra/algebra-word-problems-systems-equations-163329

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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)

2. 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.

Airplane speed: x miles per hour

Wind speed: y miles per hour

When flying with the wind, the actual speed is (x + y) mph.

(3)

When flying against the wind, the actual speed is (x - y) mph

(4)

Solving (3) and (4):

(3) + (4)

(3) - (4)

The airplane speed is 617.42 miles per hour. The wind speed is 49.24 miles per hour.

3. 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.

Cost of large soda: x dollar;

Cost of medium soda: y dollar.

The total cost is then x + y = 1.74

The large soda costs $0.016 more than the medium soda:

We have the following system

(5)

(6)

(5) + (6)

(6) - (5)

Large soda is $0.878, medium soda is $0.862.

I don't think the numbers are reasonable. In stead of $0.016, the large soda could be $0.16 more than the medium one.

Try to solve the equations using 0.16. Then you should get $0.95 and $0.79 for large and medium sodas, respectively.

4. 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?

Peanut in the mixture: x pounds

Cashew in the mixture: y pounds

The total of them is 5 lb.

The cost of peanut is 1.70x dollars. The cost of cashews is 4.55y dollars. The cost of 5lb mixtures is 2.80 * 5 = 14 dollars.

So

Linear system:

(7)

(8)

Using the substitution: from (7), , substituting to (8)

So

There are 3.07 lb peanut and 1.93 lb cashew in the mixture.

https://brainmass.com/math/linear-algebra/algebra-word-problems-systems-equations-163329