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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]

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24 Nov 2005, 21:50
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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 Aâ€™s average speed was 10 miles per hour greater than that of car B, what was car Bâ€™s average speed, in miles per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 80
Director
Joined: 14 Sep 2005
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Location: South Korea
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24 Nov 2005, 22:14
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 Aâ€™s average speed was 10 miles per hour greater than that of car B, what was car Bâ€™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
Joined: 17 Oct 2005
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24 Nov 2005, 23:36
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.
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Re: PS rates [#permalink]

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24 Nov 2005, 23:51
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 Aâ€™s average speed was 10 miles per hour greater than that of car B, what was car Bâ€™s average speed, in miles per hour?

(A) 20
(B) 30
(C) 40
(D) 50
(E) 80
Director
Joined: 24 Oct 2005
Posts: 659
Location: London
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25 Nov 2005, 03:23
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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25 Nov 2005, 03:28
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 Aâ€™s average speed was 10 miles per hour greater than that of car B, what was car Bâ€™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 -_-
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Auge um Auge, Zahn um Zahn !

25 Nov 2005, 03:28
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# The time it took car A to travel 400 miles was 2 hours less

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