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bearhunter [10]
3 years ago
7

Find 5 Rational Numbers Between 1 and 2 using (a+b/2) where a=1 and b=2.

Mathematics
1 answer:
mojhsa [17]3 years ago
4 0

Answer:

There are two ways to find the rational number between any two numbers. I will tell you an easy method to find it.

As we have to find 5 rational numbers between 1 & 2

Take 5 and add 1 to it i.e. 5+1= 6

Now take the first number and multiply and divide it by 6 i.e.

1x6/6 = 6/6

Also take the second number and multiply and divide it by 6 i.e.

2x6/6= 12/6

This is done to convert 1 & 2 into rational number i.e. in form of p/q

Now we have two numbers 6/6 and 12/6 so five rational numbers between them are

7/6, 8/6, 9/6, 10/6, 11/6

The values of these number you can check will be between 1 & 2. Actually between any two number there are infinite number of rational numbers.

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recalling that d = rt, distance = rate * time.


we know Hector is going at 12 mph, and he has already covered 18 miles, how long has he been biking already?


\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 12&1\\ 18&x \end{array}\implies \cfrac{12}{18}=\cfrac{1}{x}\implies 12x=18\implies x=\cfrac{18}{12}\implies x=\cfrac{3}{2}


so Hector has been biking for those 18 miles for 3/2 of an hour, namely and hour and a half already.

then Wanda kicks in, rolling like a lightning at 16mph.

let's say the "meet" at the same distance "d" at "t" hours after Wanda entered, so that means that Wanda has been traveling for "t" hours, but Hector has been traveling for "t + (3/2)" because he had been biking before Wanda.

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\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hector&d&12&t+\frac{3}{2}\\[1em] Wanda&d&16&t \end{array}\qquad \implies \begin{cases} \boxed{d}=(12)\left( t+\frac{3}{2} \right)\\[1em] d=(16)(t) \end{cases}


\bf \stackrel{\textit{substituting \underline{d} in the 2nd equation}}{\boxed{(12)\left( t+\frac{3}{2} \right)}=16t}\implies 12t+18=16t \\\\\\ 18=4t\implies \cfrac{18}{4}=t\implies \cfrac{9}{2}=t\implies \stackrel{\textit{four and a half hours}}{4\frac{1}{2}=t}

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