Today’s question is one I did with a student last week about petrol consumption.. and it comes with a confession – I got a bit brain-tied when I first tried to do it. This can happen to anyone.
Its not a spectacularly difficult question – though all question can seem difficult if you can’t see how to do it straight off.
My student started with the right step, by highlighting the important information. That was good start, I said, commented on what the units for ‘consumption’ were, and then my brain froze.
I unfroze it later so lets have a look at what to do.
Deal with the first 9 minutes first. What is the speed? Well, whenever you see a situation where it is a ‘mile a minute’ – just think 60mph, since there are 60 minutes in an hour. Makes thinks quicker that way.
At that speed – which is less than 65 mph, we use the first line of data.
1 gallon will take us 50 miles at that speed, but we are going nowhere near that far – just 9 miles. So the amount of petrol used will be 9/50 of a gallon – which is 0.18 gallons.
The next part we are given the speed, 70mph, so we know it is the second line of the data we need. First though we need to know the distance. 1 Hour 36 minutes = 1.6 Hours. 36/60 is 0.6 of an hour, and that makes its easier to do the calculation.
70 x 1.6 = 112 miles.
[You could do this on your calculator. I’m always looking for short cuts, and I notice that this is the same as 16 x 7 which I can do with my times tables]
At this speed, we would use more than 1 gallon, because 1 gallon will only get us to 40 miles; 2 gallons 80 miles…. or to put it another way, divide our number of miles by 40 which gives us 2.8 gallons.
Now look at the petrol used in bother parts of the journey. This gives us 2.98 gallons.
This is less tan 3 gallons, which is what the question asked us to do.
With many questions that say ‘show that’, its best to leave thinking about what you are ‘showing’ until the end.
Then split the journey in two. Don’t try doing a whole question in one when you can split it into parts.