Time speed & work............

pzazz12 wrote:Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference.After how many minutes are the three of them together again?

A. 5 mins
B. 10 mins
C. 15 mins
D. 3 mins
E. 7 mins


help me to solve it......

IMO A.

I see that you can get the answer by assuming that they meet at the starting point, but how can you assume that they meet at the starting point. Is there any way we can solve this problem by equations?

pzazz12 wrote:Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 300 feet in circumference.After how many minutes are the three of them together again?

A. 5 mins
B. 10 mins
C. 15 mins
D. 3 mins
E. 7 mins


help me to solve it......

Rates per minute for the 3 friends:
60*1 = 60ft/min
60*3 = 180ft/min
60*6 = 360ft/min.

Now we can plug in the answers, which represent the time spent traveling around the track. We should start with the smallest answer choice.

Answer choice D:
60*3 = 180 ft.
180*3 = 540 feet = 1 lap + 240 ft.
Doesn't work.

Answer choice A:
60*5 = 300 ft = 1 lap
180*5 = 900 ft. = 3 laps
360*5 = 1800 ft. = 6 laps
Success!

The correct answer is A.

I think that plugging in the answers is just as quick as -- if not quicker than -- coming up with an equation that we would then have to solve.