Chapter 4.6, Problem 56E

To determine

To find: The time for waiting for train

Answer to Problem 56E

The time for waiting for train is 6.6 minute.

Explanation of Solution

Given:

Consider the train stops at a station every 12 minutes starting at 6:00 A.M. You arrive at the station at 7:29 AM.

Calculation:

Let us assume that the common difference in time to stop the train at station d is 12 minute, and the first time $a_1$ when train starts is 6:00 A.M.

So, consider the difference and the first term and write the function represents the stop number and the time

  $f\left(n\right)=a_1+\left(n-1\right)d$

Put the value $d=12$ and $a_1=6.00$

  $f\left(n\right)=6.00+\left(n-1\right)\left(12\right)$

Now, find the stop number at which the time is 7:29 A.M. using above function

  $7.29=6.0+\left(n-1\right)\left(0.2\right)$

Multiply the terms

  $7.29=6.0+0.2n-0.2$

Take the variable at one side and find the value

  $0.2n=1.49$

Divide by 0.2 on both sides

  $n=7.45$

So, the stop number will be 8 for the train you will get

Now, the time for the $n=8$

  $\begin{array}{l}f\left(8\right)=6.0+\left(8-1\right)\left(0.2\right)\hfill \\ =6.0+1.4\hfill \\ =7.4\hfill \end{array}$

So, the time you have to wait for the train is

  $\begin{array}{l}7.40-7.29=0.11hr\hfill \\ =6.6min\hfill \end{array}$

Conclusion:

Therefore, the time for waiting for train is 6.6 minute.