Think i have fixed that question at 5 miles, think im overly panicking! Has anyone got any tips at all for these questions....definitely a mathmatical douche here.
Hi,
I think you can tackle this problem in two different ways:
1. distance = speed * time, so distance = 75 * 4 = 300. But then you need to divide this by 60, which in this case is easy: 300 / 60 = 5 miles (if you can't do this in your head, just do 30 / 6 instead, i.e., just memorize the 6 times table).
2. The math in this example is easy, but if you get a harder division you will be losing a lot of precious time. I personally prefer to think like this:
One hour is 60 minutes. So, 1/2 an hour is 30 minutes; 1/3 of an hour is 20 minutes; 1/4 of an hour is 15 minutes; 1/5 of an hour is 12 minutes; 1/6 of an hour is 10 minutes; and so on. Just memorize this.
So, if they ask for
4 minutes, you just need to relate that to one of these mentioned above (it may not be immediate). In this case, if 1/5 of an hour is 12 minutes, then
4 minutes = (1/5 of an hour) / 3, because 12 / 3 = 4, right?
Therefore, if you travel 75 miles in 1 hour, then you travel 75 / 5 miles in 1/5th of an hour (12 minutes): 75 / 5 = 15. To obtain 4 minutes, just divide again by 3 (this is really the "trick"): 15 / 3 = 5.
You could have also immediately divided 75 by 15, because 1/3 of 1/5 is 1/15, but it is harder to divide 75 by 15 than 75 by 5 and then by 3.
I really cannot explain this in a better way. This method seems complicated for this particular question, because the math is straightforward. But if you get into more complicated examples, it usually simplifies things because you break down the math into simpler calculations.
I'll just show another example:
At 15 mph, how far do you travel in 2 hours 20 minutes?
In 2 hours you travel 15 * 2 = 30 miles. Then you need to find the extra 20 minutes. Like I said, 20 minutes is 1/3 of an hour. So, in 20 minutes you travel 15 / 3 = 5 miles. Final result: 30 miles + 5 miles = 35 miles.
You could also have done this: if 1 hour = 60 minutes, then 2h20m = 140 minutes. So, 15 * 140 = 2100, and 2100 / 60 = 35 miles.
Notice how easier it is to apply the first method in this case. It is straightforward and you don't lose any time multiplying or dividing stuff.
Now imagine the question is "at 15 mph, how far do you travel in 2 hours 54 minutes?"
In this case, since 54 is not straightforward, you need to find a relation between 54 and the hour, like I've done with the 4 minutes in the other example. In that example, I used 4 = 12 / 3. Now you should use 6 * 9 = 54. As 6 is 1/10 of an hour, 54 minutes is 1/10 * 9 = 9/10 of an hour. So, in 54 minutes, you travel (15 * 9) / 10 = 13.5 miles. Now just add this to the other 30 miles (15 mph * 2 hours) and you get 43.5 miles.
In the end, I just think you need to choose the method which will save you more time.
I hope this helps.