SOLUTION: Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.

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Question 297072: Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 8 miles per hour. In how many hours will they be 54 miles apart? (Points :5)

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
Rate * Time = Distance

D = 54 miles.

Total distance is the distance traveled by the first boat plus the distance traveled by the second boat.

The time traveled by both boats will be the same.

We call it T.

the distance traveled by both boats is 54 miles.

The distance traveled by the first boat is equal to x (we assigned that).

the distance traveled by the second boat is equal to y (we assigned that also).

x + y = 54.

The rate of the first boat is 10 miles an hour.

the rate of the second boat is 8 miles an hour.

We have 2 equations that need to be solved simultaneously.

The first equation is:

10 * T = x

the second equation is :

8 * T = y

We also know that x + y = 54

Since x = 10 * T and y = 8 * T, we can susbtitute in the equation of x + y = 54 to get:

10 * T + 8 * T = 54

This means that 18 * T = 54 which means that T = 3.

Substituting for T in our equation gets:

10 * 3 + 8 * 3 = 54 which becomes 30 + 24 = 54 which becomes 54 = 54 which is true.

The boats will be 54 miles apart in 3 hours.

The first boat will have traveled 30 miles in 3 hours at 10 miles per hour.

The second boat will have traveled 24 miles in 3 hours at 8 miles per hour.

Since they are going in opposite directions, the total distance between them will be 30 + 24 = 54 miles in 3 hours.