Maurice drove 400 km from Edmonton to Battleford in 1 hour less time than it took Martin to drive the same route from Battleford to Edmonton. If Maurice drove 20 km/h faster than Martin, at what speed did each of them drive?
Show a complete algebraic solution.
Let Maurice's speed be V1
Let Martin's speed be V2
V1 = V2 + 20
elapsed times:
Morris' time = Martin's time + 1
400/V2 = 400/V1 + 1
Susbtitute for V1:
400/V2 = 400/(V2 + 20) + 1
Solve for V2; then V1
so I got up to:
V2 = (V2 + 20) + 1
right? because 400 cancells out?!?!?
I'm confused.
I can help you with the remaining steps of the algebraic solution.
You correctly set up the equation:
400/V2 = 400/(V2 + 20) + 1
Now, we can simplify this equation and solve for V2.
To simplify, we need to get rid of the fractions by finding a common denominator. The common denominator here is V2(V2 + 20):
400(V2 + 20) = 400V2 + V2(V2 + 20)
Expanding the equation:
400V2 + 8000 = 400V2 + V2^2 + 20V2
Combining like terms:
V2^2 + 20V2 + 8000 = 0
To solve this quadratic equation, we can use the quadratic formula:
V2 = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 1, b = 20, and c = 8000. Plugging in these values, we get:
V2 = (-20 ± √(20^2 - 4(1)(8000))) / (2(1))
Simplifying further:
V2 = (-20 ± √(400 - 32000)) / 2
V2 = (-20 ± √(-31600)) / 2
Since we cannot take the square root of a negative number in real numbers, there are no real solutions to this equation. It means there is no value of V2 that satisfies the equation.
Therefore, there is no solution to this problem according to the given information. Please verify if there's any missing or incorrect information in the problem statement.