
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 15th, 2015, 08:37 AM  #1 
Newbie Joined: May 2015 From: Canada Posts: 1 Thanks: 0  Speed/Distance/Time + Fuel Consumption
To begin, this isn't "homework" I'm preparing to take a test that will have this types of questions and I wanted to see if I could get any insight and strategies to be able to solve these as quickly and accurately as possible; even mentally if there are any methods (for more complicated types) So, obviously we've got our formulas: Distance = Speed / Time Speed = Distance / Time Distance = Speed * Time Also breaking up "chunks of time" in an hour 2 of 30 mins 3 of 20 mins 4 of 15 mins 5 of 12 mins 10 of 6 mins 12 of 5 mins 15 of 4 mins 20 of 3 mins 30 of 2 mins An example of an easy question to do mentally would be: Speed of 24 mph, how far would you travel in 1 hour 15 minutes? 0.25 of 24 is 6. Therefore, 24+6 = 30 miles I'm wondering if anyone knows the quickest most efficient way to solving questions such as: What speed covers 18 miles in 54 minutes And if there's a simple way to do it mentally? I appreciate your replies! This site has some sample tests including the fuel consumption questions too. Speed Distance Time  OASC: RAF Officer and Aircrew Selection Centre Here's a fuel consumption question that I'm wondering what the quickest method to solve would be: You travel 111 miles. How much fuel will you need if you burn 36 kgs per hour, and are travelling at 148 mph? 
May 15th, 2015, 09:09 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,949 Thanks: 1555  Quote:
in 6 minutes at the above rate, you travel 2 miles ... speed is 20 mph Quote:
(111 miles)/(148 miles per hr) = (x kgs)/(36 kgs per hr) x = (36 $\times$ 111)/148  
May 15th, 2015, 09:15 AM  #3  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,156 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
I don't have any particular hints other than to practise lots of questions and to experiment with the numbers if the answer isn't clear. Most of these sorts of questions are about proportions and fractions, so try to identify fractions and swot up on your times tables. Here's some specifics related to your post: Quote:
speed = distance / time distance = speed*time time = distance / speed Quote:
Basically, we want to be able to have something in miles per hour, so we want to multiply both sides by some number so that 54 minutes ends up as 60 minutes (i.e. 1 hour). So what is this number? Well, 54 minutes is 6 minutes short of an hour. 6 minutes is 1/10th of an hour, so 54 minutes represents 9/10 of an hour Therefore, 54 * 10/9 = 60 Applying the same to the lefthand side, we have 18 * 10/9 = ? ... 18/9 = 2 2*10 = 20 so the answer is 20mph. Another way of doing it is to spot that 18 goes into 54 three times. So use some ratios: 18 miles : 54 minutes (divide by 18 ) 1 mile : 3 minutes (multiply by 20) 20 miles : 60 minutes ... 20 mph. Quote:
111 happens to be three quarters of 148. .... Note: I wouldn't expect anyone to find this immediately apparent! This is how I mentally worked this out. I decided to try subtracting the two numbers (148111) to get 37. I then compared 37 with the two numbers to see if 37 would go into the two numbers. It turns out 37 goes into 111 three times (90+27)and into 148 four times (120+28 ), so I sort of recognised the 3/4 this way. In the first question I did the same. I subtracted the 54 from 60 to get 6. Note that this trick won't always work... it just helps to see what the fraction might be. Try looking over previous homeworks involving simplifying fractions and see if you can do them in your head. Anyways... Because 111 miles were travelled at 148 mph, the person journeyed for 3/4 of an hour. Therefore, 3/4 of the fuel was burnt. 3/4 of 36 = ? 36/4 = 9 9*3 = 27 So the answer is 27kg. Last edited by Benit13; May 15th, 2015 at 09:21 AM.  
May 15th, 2015, 01:59 PM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
 
November 8th, 2015, 01:31 PM  #5 
Newbie Joined: Nov 2015 From: Texas Posts: 1 Thanks: 0  Fuel cost calculator
A good cost calculator there is in Route between cities  calculatemyroute.com e.g From New York City to Albany 152 mi, 2 hours 38 mins petrol: Fuel consumption: 4.8 gal Fuel price: 2.46 dollar per gal Vehicle consumption: 31.4 mpg Fuel cost: 11.81 dollar diesel: Fuel consumption: 2.9 gal Fuel price: 2.5 dollar per gal Vehicle consumption: 52.3 mpg Fuel cost: 7.25 dollar 
November 21st, 2015, 03:58 PM  #6 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  

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