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The time it took car A to travel 400 miles was 2 hours less

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Director
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The time it took car A to travel 400 miles was 2 hours less [#permalink] New post 24 Nov 2005, 20:50
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A
B
C
D
E

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The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A’s average speed was 10 miles per hour greater than that of car B, what was car B’s average speed, in miles per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 80
Director
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Location: South Korea
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 [#permalink] New post 24 Nov 2005, 21:14
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A’s average speed was 10 miles per hour greater than that of car B, what was car B’s average speed, in miles per hour?

A's travelling time = X
B's travelling time = X + 2
A's speed = Y
B's speed = Y - 10
Distance = 400

Speed = Distance / Time

Distance = Speed * Time

400 = XY
400 = (X+2) * (Y-10)

XY = XY - 20 + 2Y - 10X

20 - 2Y + 10X = 0

10 - Y + 5X = 0

Y = 5X + 10


Speed = Distance / Time


B's speed = Y - 10 = 5X + 10 - 10 = 5X
B's speed = 400 / (X+2)

5X = 400/(X+2)

X = 80/(X+2)

X^2 + 2X - 80 = 0

(X+10)(X-8)=0

X = -10 or X = 8

X has to be positive.

X = 8.


Therefore, B's speed is 80m/h. (E)
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Director
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 [#permalink] New post 24 Nov 2005, 22:36
A B

t-2 t
s+10 s

st=400

(t-2)(s+10)=400

ts-2s-20+10t=ts

2s+20-10t=0

s=-10+5t t=400/s

-10+5(400/s)=s

s^2 +10s -2000=0

(s+50)(s-40)
s=40

The answer is C.
Director
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Re: PS rates [#permalink] New post 24 Nov 2005, 22:51
C
took just 40 second by backsolving...

total distance 400 miles..
start with B , let carB speed = 30
time taken = 400/30=13.33
we know car A speed with 10 greater than B so A = 40
Time taken = 400/40=10 ( time difference greater than 2 hour wrong)

try C , Car B speed 40 , time taken 10 hours
then Car A speed 50 , time taken 8 hours ...which is 2 hours less....

so ...ans C


joemama142000 wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A’s average speed was 10 miles per hour greater than that of car B, what was car B’s average speed, in miles per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 80
Director
Director
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Posts: 663
Location: London
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 [#permalink] New post 25 Nov 2005, 02:23
Got 40.

Solved the 2 equations

A's case --> (s+10) (t-2) = 400
B's case --> st =400

Time = 10
Speed = 40
Director
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 [#permalink] New post 25 Nov 2005, 02:28
gamjatang wrote:
The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A’s average speed was 10 miles per hour greater than that of car B, what was car B’s average speed, in miles per hour?

A's travelling time = X
B's travelling time = X + 2
A's speed = Y
B's speed = Y - 10
Distance = 400

Speed = Distance / Time

Distance = Speed * Time

400 = XY
400 = (X+2) * (Y-10)

XY = XY - 20 + 2Y - 10X

20 - 2Y + 10X = 0

10 - Y + 5X = 0

Y = 5X + 10


Speed = Distance / Time


B's speed = Y - 10 = 5X + 10 - 10 = 5X
B's speed = 400 / (X+2)

5X = 400/(X+2)

X = 80/(X+2)

X^2 + 2X - 80 = 0

(X+10)(X-8)=0

X = -10 or X = 8

X has to be positive.

X = 8.


Therefore, B's speed is 80m/h.
(E)


Where does this number "80" come from???

If X = 8, then (X+2) = 10.

400/10 = 40. It should be 40.

I was a complete fool here -_- :oops:
_________________

Auge um Auge, Zahn um Zahn :twisted: !

  [#permalink] 25 Nov 2005, 02:28
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