+0  
 
0
74
2
avatar

  

At 3 p.m , four runners all leave the starting line, running laps around the indoor track.If the runners maintain their pace, at what time will Sue,Drew, and Ste finish a lap together? At what time will all 4 runners finish a lap together? Explain your reasoning

Sue lap 1 time- 1.30

Drew lap 1 time- 2.00

Stu lap 1 time- 1.12

Marylou lap 1 time- 1.20

Guest Jun 6, 2017

Best Answer 

 #1
avatar+75316 
+1

 

Note that

 

Sue lap 1 time- 1.30  →  runs  2/3  of a lap in one minute  

Drew lap 1 time- 2.00  → runs 1/2 of a lap in one minute 

Stu lap 1 time- 1.12 → runs 60/72 =  5/6 of a lap in one minute    

Marylou lap 1 time- 1.20 → runs 3/4  of a lap in one minute  

 

So ...getting a common denominator between their rates, we have that

 

Sue  =  4/6  laps in one minute   =    8/ 12  of a lap in one minute

Drew =  3/6  laps in one minute  =  6/12 of a lap in one minute

Stu = 5/6  laps in one minute  = 10/12 of a lap in one minute

Marylou  =  3/4 lap in one minute = 9/12 of a lap in one minute

 

So...in 6 minutes  [at 3:06 PM ] 

Sue will have run 4 laps, Drew will have run 3 laps and Stu will have run 5 laps...and they are all back at the starting line

 

And in 12 minutes [ at 3:12 PM]

Sue will have run 8 laps, drew will have run 6 laps, Stu will have run 10 laps and Marylou will have run 9 laps...and they are all back at the starting line

 

 

 

cool cool cool

CPhill  Jun 6, 2017
Sort: 

2+0 Answers

 #1
avatar+75316 
+1
Best Answer

 

Note that

 

Sue lap 1 time- 1.30  →  runs  2/3  of a lap in one minute  

Drew lap 1 time- 2.00  → runs 1/2 of a lap in one minute 

Stu lap 1 time- 1.12 → runs 60/72 =  5/6 of a lap in one minute    

Marylou lap 1 time- 1.20 → runs 3/4  of a lap in one minute  

 

So ...getting a common denominator between their rates, we have that

 

Sue  =  4/6  laps in one minute   =    8/ 12  of a lap in one minute

Drew =  3/6  laps in one minute  =  6/12 of a lap in one minute

Stu = 5/6  laps in one minute  = 10/12 of a lap in one minute

Marylou  =  3/4 lap in one minute = 9/12 of a lap in one minute

 

So...in 6 minutes  [at 3:06 PM ] 

Sue will have run 4 laps, Drew will have run 3 laps and Stu will have run 5 laps...and they are all back at the starting line

 

And in 12 minutes [ at 3:12 PM]

Sue will have run 8 laps, drew will have run 6 laps, Stu will have run 10 laps and Marylou will have run 9 laps...and they are all back at the starting line

 

 

 

cool cool cool

CPhill  Jun 6, 2017
 #2
avatar
0

Sue lap 1 time- 1.30

Drew lap 1 time- 2.00

Stu lap 1 time- 1.12

Marylou lap 1 time- 1.20

 

I assume the times of their laps are in minutes and seconds. If that is so, then we have:

LCM{90, 120, 72, 80} =720 seconds, or:

720 / 60 =12 minutes - or 3:12 pm when they will finish together.

Guest Jun 6, 2017

12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details