My Math Forum Find the ratio of his usual speed to his speed that day.

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 January 15th, 2014, 11:05 PM #1 Senior Member     Joined: Jan 2012 Posts: 725 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 round-round-trip, (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: 2,780 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: 390 Thanks: 70 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: 390 Thanks: 70 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
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Re: Find the ratio of his usual speed to his speed that day.

Quote:
 Originally Posted by Timios On that day, to go 1200 km to 16h. 1200/16=75 So his speed that day was 75km/h
Why don't you use 2*1200 km in the numerator?

 January 21st, 2014, 12:56 PM #6 Senior Member     Joined: Jan 2012 Posts: 725 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
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Re: Find the ratio of his usual speed to his speed that day.

Quote:
 Why don't you use 2*1200 km in the numerator?
I didn't because I didn't read the problem carefully enough.

January 22nd, 2014, 02:16 AM   #8
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Re: Find the ratio of his usual speed to his speed that day.

Quote:
 Originally Posted by Timios I didn't because I didn't read the problem carefully enough.
Okay, just checking if I didn't miss anything

January 22nd, 2014, 02:25 AM   #9
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Re: Find the ratio of his usual speed to his speed that day.

Quote:
 Originally Posted by Chikis what principle guided you into using the method that used in your alernative working which gave you answer as the first method?
You are merely asked for a comparison between two speeds. How much times faster was the round-round-trip than the usual trip on average.

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 round-round-trip distance would be 2D and the round-round-trip 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: 725 Thanks: 7 Re: Find the ratio of his usual speed to his speed that day. Hi Hoempa, How would the round-round-trip time be 4D/3? I understand.

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