Chapter 5.2, Problem 5STP

The distance $d$ a train travels varies directly with the amount of time $t$ that has elapsed since departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after 4 hours?

To determine

To calculate: Distance travelled by train in 4 hours.

Answer to Problem 5STP

200 miles.

Explanation of Solution

Given information: d varies directly with t.

Distance travelled by train in 9.5 hours is equal to 475 miles.

Calculation:

As distance travelled d varies directly with the amount of time t,

  $d=kt$ where $k$ is a constant of proportionality

As distance travelled by train in 9.5 hours is equal to 475 miles, put $d=475,t=9.5$ in $d=kt$

  $\begin{array}{l}475=9.5k\\ \Rightarrow k=\frac{475}{9.5}\\ =50\end{array}$

So,

  $d=50t$

In order to find distance travelled by train in 4 hours, put $t=4$ in $d=50t$

  $d=50(4)=200$ miles

Therefore,

Distance travelled by train in 4 hours is equal to 200 miles.