800guy wrote:OA coming when a few people have answered...

**A and B ran 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 Bï¿½s speed in m/s?**

(A) 12

(B) 14

(C) 16

(D) 18

(E) 20

We can plug in the answers, which represent B's rate.

The correct answer must be a factor of 480.

Eliminate B and D.

In the first heat, A beats B by (1/10)*60 = 6 seconds.

In the second heat, B beats A by (1/30)*60 = 2 seconds.

**Answer choice C: B = 16 meters per second.**
First heat:

Time for B = d/r = 480/16 = 30 seconds.

Headstart given to A = 48/16 = 3 seconds.

Since A beats B by 6 seconds, total time for A = 30-(3+6) = 21 seconds.

21 is not a factor of 480.

Eliminate C.

**Answer choice A: B = 12 meters per second.**
First heat:

Time for B = d/r = 480/12 = 40 seconds.

Headstart given to A = 48/12 = 4 seconds.

Since A beats B by 6 seconds, total time for A = 40-(4+6) = 30 seconds.

Rate for A = d/t = 480/30 = 16 meters per second.

Second heat:

Headstart given to B = 144/12 = 12 seconds.

From the first heat: Time for B - Time for A = 40-30 = 10 seconds.

Since B is given a 12-second headstart, and the time for A is only 10 seconds less than the time for B, B beats A by 12-10 = 2 seconds.

Success!

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