SOLUTION: Hello. I seem to have particular trouble with word problems. I can't develop the equation so I never get to the point of solving it. Each time I do it correctly, it seems like a fl

Question 237530: Hello. I seem to have particular trouble with word problems. I can't develop the equation so I never get to the point of solving it. Each time I do it correctly, it seems like a fluke and I can't recreate it. I'd appreciate any help you can offer.
Here is the question:
Suppose that Car A can travel 250 miles in 3 hours less time than it takes Car B to travel 440 miles. The rate of Car B is 5 miles per hour faster than that of Car A. Find the rates of both cars.
Found 2 solutions by scott8148, edjones:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
time = distance / rate

(250 / A) + 3 = 440 / (A + 5)

multiplying by A(A + 5) ___ 250A + 1250 + 3A^2 + 15A = 440A

3A^2 - 175A + 1250 = 0

factoring ___ (3A - 25)(A - 50) = 0

3A - 25 = 0 ___ A = 25/3 ___ B = 40/3

A - 50 = 0 ___ A = 50 ___ B = 55
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
You picked a tough problem but we can do it.
a) what formula are you going to use? Ans.: st=d, speed * time=distance
.
b) speed
Let s-5=car A's speed
Let s=car B's speed
.
c)time
Let t=car B's time
.
We can make a system of equations now. Look at the formula for B 1st because it is the simplest.
A) (s-5)(t-3)=250
B) st=440
.
B) s=440/t
A)
(440/t -5)(t-3)=250 Substitute 440/t for s
(440-5t)(t-3)=250t multiply t times each side to eliminate the fraction.
-5t^2+455t-1320=250t
t^2-91t+264=-50t Divide each side by -5
t^2-41t+264=0
(t-8)(t-33)=0 Factor
t=8 hrs, t=33 hrs
If we use t=8 then for B: s=440/8=55mph
Then for A: s=50mph
.
Check:
A travels 250 mi in 5h
B travels 440 mi in 8h which is 3hrs longer than A traveling 250mi.
.
Ed

.
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