SOLUTION: Vehicle A travels at x miles per hour for x hours. Vehicle B travels a miles per hour faster than Vehicle A, and travels b hours longer than Vehicle A. Vehicle B travels how much f

Question 1190421: Vehicle A travels at x miles per hour for x hours. Vehicle B travels a miles per hour faster than Vehicle A, and travels b hours longer than Vehicle A. Vehicle B travels how much faster than Vehicle A, in miles?
A) x^2-ab
B) a^2+b^2
C) ax+ax+ab
D) x^2+abx+ab
E) 2x^2+(a+b)x+ab
Found 2 solutions by math_tutor2020, Theo:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

You already stated that
"Vehicle B travels a miles per hour faster than Vehicle A"
which means it doesn't make sense why you ask about Vehicle B's speed in your last sentence.

For the last sentence, I'm assuming that you meant to say
"Vehicle B travels how much further than Vehicle A, in miles?"

Distance = Rate*Time
Rate = speed

Vehicle Distance Speed Time
A x^2 x x
B (x+a)(x+b) x+a x+b

Vehicle B distance = rate*time
Vehicle B distance = (x+a)(x+b)
Vehicle B distance = x^2 + bx + ax + ab
Vehicle B distance = x^2 + (a+b)x + ab

Subtract off Vehicle A's distance of x^2
B - A = (x^2 + (a+b)x + ab) - (x^2)
B - A = (a+b)x + ab
B - A = ax + bx + ab
This represents how much further vehicle B has traveled compared to vehicle A.
The units are in miles.

It looks like choice C might be a match assuming there's a typo and the ax+ax should actually be ax+bx

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe you are looking for the number of miles that vehicle A traveled more than the number of miles that vehicle B traveled.

if thwt's what you wanted, then:

vehicle a traveled x miles per hour for x hours = x^2.
vehicle b traveled (x + a) miles per hour for (x + b) hours = (x + a) * (x + b).

since rate * time = distance, then simplify both equation to get:

vehicle A traveled x^2 miles.
vehicle B traveled x^2 + bx + ax + ab miles.

to see how much farther vehicle B traveled than vehicle A, subtract vehicle A miles from vehiclle A miles to get:

x^2 + bx + ax + ab minus x^2 = bx + ax + ab.

vehicle B traveled ax + bx + ab miles further than vehicle A.

that is not one of your selections, but selection C looks suspiciously like it could be the answer, if only one of the ax in that selection was a bx.

none of the other selections are even close.

i tested out my answer by letting x = 8 and a = 1 and b = 2
i got:

vehicle A traveled for 8^2 = 64 miles.
vehicle B traveled for (8 + 1) * (8 + 2) = 9 * 10 = 90 miles.
the difference in miles was 26 miles.
ax + bx + ab = 1*8 + 2*8 + 2 = 8 + 16 + 2 = 26 miles.

the formula works with ax + bx + ab difference in miles.
that's why i think selection C is mistyped and should be ax + bx + ab rather than ax + ax + ab.

that's my opinion, of course.
check your problem out again and see if that might be right.
let me know if that's it, or thaere's some other answer being looked for.

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