A and B ran, at either respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m, and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
The OA is A.
I'm working through question 6 and the answer explanation has me lost. I'm having trouble putting the numbers together in a formula that makes sense and am not following the variables posted in the answer. Can any expert help me with this PS question, please? Thanks!
A and B ran, at their respective constant rates, a race of..
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Head start in the second heat - head start in the first heat = 144-48 = 96 meters.LUANDATO wrote:A and B ran, at either respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m, and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Thus, B travels an additional 96 meters in the first heat.
In the second heat, B travels for 2 seconds LESS than A (with the result that B WINS by 2 seconds).
In the first heat, B travels for 6 seconds MORE than A (with the result that B LOSES by 6 seconds).
Since 2+6 = 8, B travels for 8 seconds LONGER in the first heat than he does in the second heat.
Since in these 8 seconds B travels an additional 96 meters, his rate = d/t = 96/8 = 12 meters per second.
The correct answer is A.
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We can let a and b be the rates of A and B, in m/s, respectively. Since 1/10 minute = 6 seconds and 1/30 minute = 2 seconds, we can now create the equations:BTGmoderatorLU wrote: ↑Thu Dec 14, 2017 12:04 pmA and B ran, at either respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m, and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
The OA is A.
I'm working through question 6 and the answer explanation has me lost. I'm having trouble putting the numbers together in a formula that makes sense and am not following the variables posted in the answer. Can any expert help me with this PS question, please? Thanks!
480/a + 6 = (480 - 48)/b
and
480/a - 2 = (480 - 144)/b
Subtracting the two equations, we have:
8 = (480 - 48)/b - (480 - 144)/b
8 = 432/b - 336/b
8 = 96/b
8b = 96
b = 12
Answer: A
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