Question

A plane travels $5100km$ in $6$ hours. How far will it go in $4$ hours $36$ minutes ?

Answer 1

Step 1: Convert hours into minutes

Given. plane travels $5100km$ in $6$ hours

Let plane travels in $4$ hours $36$ minutes $=kkm$

$6$ hours $=6\times 60=360minutes$ $[\because 1hour=60minutes]$

$4$hours$36$ minutes $=4\times 60+36$ $[\because 1hour=60minutes]$

$=240+36=276$

Step 2: How far will it go in $4$ hours $36$ minutes

As the time decreases, the distance also increases in the same ratio. So it is a case of direct proportion.

We make use of the relation of type $\frac{x_1}{x_2}=\frac{y_1}{y_2}$

Suppose the time is $\text{'}x\text{'}$ minutes and plane travels distance is $\text{'}y\text{'}.$.

$$\begin{gathered} x_1=360minutes;x_2=276minutes \\ {y}_1=5100km;y_2=kkm \end{gathered}$$

So, by using direct proportion law, we get

$$\begin{gathered} \frac{360}{276}=\frac{5100}{k} \\ 360\times k=5100\times 276 \\ k=\frac{{\displaystyle \stackrel{85}{\cancel{5100}}}\times {\displaystyle \stackrel{46}{\cancel{276}}}}{{\displaystyle \underset{\cancel{6}}{\cancel{360}}}} \\ k=3910km \end{gathered}$$

Hence the distances covered in $4$ hours $36$ minutes is $3910km$.