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January 15th, 2014, 11:05 PM  #1 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Find the ratio of his usual speed to his speed that day.
A taxi driver usually does a trip of 1,200km in 12hrs. On a day he was to do a roundroundtrip, (i.e., do the trip and return to base) he used 16 hrs for the round trip. Find the ratio of his usual speed to his speed that day.

January 16th, 2014, 05:34 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: Find the ratio of his usual speed to his speed that day.
Usually, 1,200km / (12 hour) = 100 km/hour One day, 2*1,200 km / (16 hour) = 150 km/hour. Usual speed : his speed that day = 100 km/hour : 150 km/hour = 2 : 3 Alternatively speed = distance / time On a day, the distance was twice as long, time was 16/12 = 4/3 times as long, so speed was 2/(4/3) = (2*3)/4 = 3/2 times as fast, so ratio Usual speed : his speed that day = 2 : 3 
January 18th, 2014, 07:44 PM  #3 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68  Re: Find the ratio of his usual speed to his speed that day.
Usual speed was 100 km/h On that day, to go 1200 km to 16h. 1200/16=75 So his speed that day was 75km/h The ratio of his usual speed to his speed on that day was 100:75 That ratio would reduce to 4:3 
January 18th, 2014, 07:46 PM  #4 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68  Re: Find the ratio of his usual speed to his speed that day.
I meant "On that day, to go 1200 km took 16h.

January 19th, 2014, 11:12 AM  #5  
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: Find the ratio of his usual speed to his speed that day. Quote:
 
January 21st, 2014, 12:56 PM  #6 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Re: Find the ratio of his usual speed to his speed that day.
Hi Hoempa, I think I understand, checked and agree with you that your working and answers are correct. I.e as it has to do with your first working. I have no problem undestanding the first method. But there is one mystery which am yet to unravel. And that mystery is what principle guided you into using the method that used in your alernative working which gave you answer as the first method? 
January 21st, 2014, 08:42 PM  #7  
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68  Re: Find the ratio of his usual speed to his speed that day. Quote:
 
January 22nd, 2014, 02:16 AM  #8  
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: Find the ratio of his usual speed to his speed that day. Quote:
 
January 22nd, 2014, 02:25 AM  #9  
Math Team Joined: Apr 2010 Posts: 2,778 Thanks: 361  Re: Find the ratio of his usual speed to his speed that day. Quote:
Now, speed is distance / time. So we can do two things.  compute both speeds and divide to get the proper ratio. Compute the actual speed. I'll avoid the word absolute for that.  use the changes of distance and time, arguments to compute the speed and divide them. It's as if you where initially told his usual trip would be D kilometers and would take him T hours. Then you would know his roundroundtrip distance would be 2D and the roundroundtrip time would be 4D/3. But we just knew the values for D and T. This is the priniciple I used in the alternative method. Got it?  
January 23rd, 2014, 06:11 PM  #10 
Senior Member Joined: Jan 2012 Posts: 720 Thanks: 7  Re: Find the ratio of his usual speed to his speed that day.
Hi Hoempa, How would the roundroundtrip time be 4D/3? I understand. 

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