91Ó°ÊÓ

The relationship between the distance and time is given as directly proportional.

Use the given sentence to find the required relation.

• As given, the distance is directly proportional to the time hence $d\mathrm{Î\pm }t$.
• Convert the proportionality into equality with the help of the proportional constant k.
• Hence the required equation for the variation is $d=kt...........\left(1\right)$.
• As given, the distance travelled in 2 hours is 100 miles hence substitute $d=100,t=2$into equation (1).

$\begin{array}{rcl}d& =& kt\\ 100& =& k\left(2\right)\\ \frac{100}{2}& =& k\\ k& =& 50\end{array}$

Hence substitution of k into equation (1) gives the variation equation$d=50t...........\left(2\right)$.

Apply the substitution of the time into equation (2) to find the distance traveled.

• Substitute time by 5 into equation (2) and solve to find the distance.

$\begin{array}{rcl}d& =& 50t\\ & =& 50\left(5\right)\\ & =& 250miles\end{array}$