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A and B ran, at their respective rates, a race of 480m...

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by BTGmoderatorLU » Sat Mar 10, 2018 1:45 pm
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.
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by mbawisdom » Sat Mar 10, 2018 2:15 pm
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.
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.

Cheers,
Dan
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by Brent@GMATPrepNow » Mon Mar 12, 2018 7:15 am
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
Here's one approach. . .
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by deloitte247 » Sun Mar 18, 2018 10:48 am
when A gives B a head set of 48m, A ran 480m in, say, x seconds and
B ran (480-48)m =432m in
$$x+\frac{60}{10}=\left(x+6\right)\sec$$
$$B's\ rate\ can\ thus\ be\ \exp ressed\ as\ 432m\ in\ \left(x+6\right)s=\left(\frac{432}{x+6}\right)\ \frac{m}{s}$$
$$when\ A\ gives\ B\ a\ head\ start\ of\ 144m,$$
$$A\ ran\ 480m\ in\ the\ same\ x\ \sec onds,$$
$$and\ B\ ran\ 480-144m\ =\left(336m\right)\ in\ x-\frac{60}{30}=\left(x-2\right)\sec onds$$
$$B's\ rate\ can\ be\ \exp ressed\ as\ \left(\frac{336}{x-2}\right)\ \frac{m}{s}$$
$$Equating\ B's\ rate:\ i.e\ \frac{432}{x+6}=\frac{336}{x-2}$$
$$432\left(x-2\right)=336\left(x+6\right)\ \ ;\ dividing\ through\ by\ 48,\ we\ have$$
$$9\left(x-2\right)=7\left(x+6\right)=\ 9x-18=7x+42\ $$
$$or\ 9x-7x=60$$
$$x=\frac{60}{2}=30s$$
$$Therefore,\ B's\ rate=\frac{436}{30+6}\ \frac{m}{s}\ =12\ \frac{m}{s\ }\ \left[option\ A\right]$$
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by Jeff@TargetTestPrep » Tue Mar 20, 2018 4:08 pm
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
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:

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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