My Math Forum Speed/Distance/Time + Fuel Consumption

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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
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Quote:
 What speed covers 18 miles in 54 minutes
every 6 minutes, you travel 1/10 of the distance traveled by the speed in 1 hour ...

in 6 minutes at the above rate, you travel 2 miles ... speed is 20 mph

Quote:
 You travel 111 miles. How much fuel will you need if you burn 36 kgs per hour, and are travelling at 148 mph?
I would use a ratio, and most folks would need a calculator for this one ...

(111 miles)/(148 miles per hr) = (x kgs)/(36 kgs per hr)

x = (36 $\times$ 111)/148

May 15th, 2015, 09:15 AM   #3
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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:
 Originally Posted by RCAF91 So, obviously we've got our formulas: Distance = Speed / Time Speed = Distance / Time Distance = Speed * Time
Be careful... it's

speed = distance / time
distance = speed*time
time = distance / speed

Quote:
 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 don't know if there's a proven "most efficient" way of doing it because people's heads all work in different ways, but this is how I did it:

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 left-hand side, we have
18 * 10/9 = ?
...
18/9 = 2
2*10 = 20

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:
 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?
hmmmm...

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 (148-111) 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

Last edited by Benit13; May 15th, 2015 at 09:21 AM.

May 15th, 2015, 01:59 PM   #4
Math Team

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From: Alabama

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Quote:
 What speed covers 18 miles in 54 minutes And if there's a simple way to do it mentally?
For this one in particular, 18= 9(2) and 54= 9(6) so speed= 18 miles/ 54 minutes= 2 miles/6 minutes= 1 mile/3 minutes. There are 60= 3(20) minutes in an hour so 1 mile/3 minutes= 20 miles/hour.

 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
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Math Focus: Trigonometry
Quote:
 Originally Posted by Benit13 Be careful... it's speed = distance / time distance = speed*time time = distance / speed
For the OP, in case you mixed them up again, remember that the unit of speed (either kmph, mph, or mps) is the unit of distance divided by the unit of time.

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