SOLUTION: Sam's Subaru travels 280 miles at a certain speed. if the car had gone 5 mph faster, the trip would have taken 1 hour less. find Sam's speed.

Question 430757: Sam's Subaru travels 280 miles at a certain speed. if the car had gone 5 mph faster, the trip would have taken 1 hour less. find Sam's speed.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
d=rt
d=280
280 = rt
.
Going 5 mph faster makes the trip in 1 less hr, to cover the same distance.
d = (r+5)(t-1)
280 = (r+5)(t-1)
.
Since each = 280, then they have to = each other.
.
rt = (r+5)(t-1)
Multiply through on the right side.
rt = rt +5t -r - 5
Subtract rt from both sides
0 = 5t -r - 5
Add r to both sides
r = 5t-5
Substitute back into the distance equation
280 = (5t-5)*t
Expand
280 = 5t^2 -5t
Subtract 280 from both sides
0 = 5t^2 -5t - 280
Equals are equal, so you can write it either way
5t^2 -5t - 280 = 0
Factor
(5t-40)(t+7)=0
.
Inspect the solutions for applicability
.
5t = 40
t = 8, is one solution
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t = -7 is not a reasonable solution because we cannot have negative time
.
Substitute t=8 to find r
280 = r*8
Divide both sides by 8
r = 280/8
r = 35
.
Now check your work to see if the modified equation works
.
280 = (r+5)(t-1)
280 = (35+5)(8-1)
280 = (40)(7)
True
.
Re-read the question to ensure you answer it.
Sam's speed was 35 mph.
.
Done.
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