Question 1170847: Use a system of linear equations with two variables and two equations to solve.
A jeep and BMW enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 6 mph slower than the BMW. After 3 hours from the time the BMW entered the highway, the cars were 414.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.
I tried it the best I could.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this word problem into a system of linear equations.
1. Define Variables:
Let 'j' represent the speed of the jeep (in mph).
Let 'b' represent the speed of the BMW (in mph).
2. Translate the Information into Equations:
Relationship between speeds: The jeep traveled 6 mph slower than the BMW.
j = b - 6
Distance traveled:
The jeep traveled for 3.5 hours (3 hours + 30 minutes).
The BMW traveled for 3 hours.
The total distance between them is 414.5 miles.
Since they are traveling in opposite directions, the total distance is the sum of their individual distances.
Distance = speed × time.
Distance traveled by jeep: 3.5j
Distance traveled by BMW: 3b
Total distance equation: 3.5j + 3b = 414.5
3. Solve the System of Equations:
We have the following system:
j = b - 6
3.5j + 3b = 414.5
We can use substitution to solve.
Substitute the first equation (j = b - 6) into the second equation:
3.5(b - 6) + 3b = 414.5
Distribute and simplify:
3.5b - 21 + 3b = 414.5
6.5b - 21 = 414.5
Add 21 to both sides:
6.5b = 435.5
Divide by 6.5:
b = 435.5 / 6.5
b = 67
Now, substitute the value of 'b' back into the first equation to find 'j':
j = 67 - 6
j = 61
4. Answers:
The speed of the jeep (j) is 61 mph.
The speed of the BMW (b) is 67 mph.
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