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

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Question 311231: Translate the problem into a pair of linear equations in two vaiables. 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?

Found 2 solutions by OmniMaestra, mananth:
Answer by OmniMaestra(21) (Show Source):
You can put this solution on YOUR website!
First boat--> rate * time = distance
10 * t = X

Second boat-->rate * time = distance
8 * t = 54-X

Solve first boat for t:
10t = x
10t/10= X/10
t = X/10
Substitute into equation for second boat:
8t = 54-X
8(X/10)=54-X
8X/10 = 54-X
4x/5 = 54-X
5(4x/5) = 5(54-X)
4x = 270-5X
9x = 270
x = 30
Substitute new X value into equation for boat #1:
10t = X
10t = 30
t = 3
In three hours the two boats will be 54 miles apart.

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
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?
When they are at a distance of 54 miles
let boat A travel x miles
Let boat B travel y miles
x+y=54
.
Time taken by boat A will be x/10 hours
Time taken by boat B = y/8 hours
time taken by them is the same.
x/10=y/8
8x=10y
8x-10y=0
.
10(x+y)+(8x-10y)= 10*54+0
10x+10y+8x-10y= 540
18x=540
x= 30 Boat A travels 30 miles.
To travel 30 miles Boat A will take 30/10 hours
= 3 hours.
.
check
Boat B will travel 24 miles
Time taken by boat B = 24/8
=3 hours.
After 3 hours they will be at a distance of 54 miles