A and B ran, at their respective rates, a race of 480m. In the first heat, A gives B a head start of 48m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144m 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 confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.
A and B ran, at their respective rates, a race of 480m...
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Luandato, what are you confused about? Do let me know how you approached the question and I'd be happy to help you improve your logic. The question looks pretty similar to the other S = D/T questions you have posted before. I'll let you come back to me with your working/process and if you still need help I'll show you how I would approach the question.LUANDATO wrote:A and B ran, at their respective rates, a race of 480m. In the first heat, A gives B a head start of 48m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144m 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 confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.
Cheers,
Dan
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 Brent@GMATPrepNow
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Here's one approach. . .LUANDATO wrote:A and B ran, at their respective rates, a race of 480m. In the first heat, A gives B a head start of 48m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144m 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
Let A = A's speed in meters per second
Let B = B's speed in meters per second
A gives B a head start of 48 m and beats him by 1/10th of a minute.
1/10th of a minute = 6 seconds
A's travel time is 6 seconds less than B's travel time
So, (A's travel time) = (B's travel time)  6
A traveled 480 meters and B traveled 432 meters.
Travel time = distance/speed, so . . .
(480/A) = (432/B)  6
A gives B a head start of 144 m and is beaten by 1/30th of a minute.
1/30th of a minute = 2 seconds
A's travel time is 2 seconds more than B's travel time
So, (A's travel time) = (B's travel time) + 2
A traveled 480 meters and B traveled 336 meters.
Travel time = distance/speed, so . . .
(480/A) = (336/B) + 2
IMPORTANT: Since both equations are set equal to 480/A, we can set them equal to each other.
(432/B)  6 = (336/B) + 2
Multiply both sides by B: 432  6B = 336 + 2B
Rearrange: 96 = 8B
Solve: B = 12
Answer: A
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when A gives B a head set of 48m, A ran 480m in, say, x seconds and
B ran (48048)m =432m in
$$x+\frac{60}{10}=\left(x+6\right)\sec$$
$$B's\ rate\ can\ thus\ be\ \exp ressed\ as\ 432m\ in\ \left(x+6\right)s=\left(\frac{432}{x+6}\right)\ \frac{m}{s}$$
$$when\ A\ gives\ B\ a\ head\ start\ of\ 144m,$$
$$A\ ran\ 480m\ in\ the\ same\ x\ \sec onds,$$
$$and\ B\ ran\ 480144m\ =\left(336m\right)\ in\ x\frac{60}{30}=\left(x2\right)\sec onds$$
$$B's\ rate\ can\ be\ \exp ressed\ as\ \left(\frac{336}{x2}\right)\ \frac{m}{s}$$
$$Equating\ B's\ rate:\ i.e\ \frac{432}{x+6}=\frac{336}{x2}$$
$$432\left(x2\right)=336\left(x+6\right)\ \ ;\ dividing\ through\ by\ 48,\ we\ have$$
$$9\left(x2\right)=7\left(x+6\right)=\ 9x18=7x+42\ $$
$$or\ 9x7x=60$$
$$x=\frac{60}{2}=30s$$
$$Therefore,\ B's\ rate=\frac{436}{30+6}\ \frac{m}{s}\ =12\ \frac{m}{s\ }\ \left[option\ A\right]$$
B ran (48048)m =432m in
$$x+\frac{60}{10}=\left(x+6\right)\sec$$
$$B's\ rate\ can\ thus\ be\ \exp ressed\ as\ 432m\ in\ \left(x+6\right)s=\left(\frac{432}{x+6}\right)\ \frac{m}{s}$$
$$when\ A\ gives\ B\ a\ head\ start\ of\ 144m,$$
$$A\ ran\ 480m\ in\ the\ same\ x\ \sec onds,$$
$$and\ B\ ran\ 480144m\ =\left(336m\right)\ in\ x\frac{60}{30}=\left(x2\right)\sec onds$$
$$B's\ rate\ can\ be\ \exp ressed\ as\ \left(\frac{336}{x2}\right)\ \frac{m}{s}$$
$$Equating\ B's\ rate:\ i.e\ \frac{432}{x+6}=\frac{336}{x2}$$
$$432\left(x2\right)=336\left(x+6\right)\ \ ;\ dividing\ through\ by\ 48,\ we\ have$$
$$9\left(x2\right)=7\left(x+6\right)=\ 9x18=7x+42\ $$
$$or\ 9x7x=60$$
$$x=\frac{60}{2}=30s$$
$$Therefore,\ B's\ rate=\frac{436}{30+6}\ \frac{m}{s}\ =12\ \frac{m}{s\ }\ \left[option\ A\right]$$
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We can let a = A's speed in m/s and b = B's speed in m/s. Notice that 1/10th of a minute = 6 seconds and 1/30th of a minute = 2 seconds. Since time = distance/rate, we have:LUANDATO wrote:A and B ran, at their respective rates, a race of 480m. In the first heat, A gives B a head start of 48m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144m 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
480/a = (480  48)/b  6
and
480/a = (480  144)/b + 2
Setting them equal to each other, we have:
(480  48)/b  6 = (480  144)/b + 2
432/b  6 = 336/b + 2
Multiplying both sides by b, we have:
432  6b = 336 + 2b
96 = 8b
12 = b
Answer: A
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