Chapter 11.5, Problem 44PPS

(a)

To determine

To calculate: To write an expression for the amount of time that each van has spent on the road after an additional $t$ minutes

Answer to Problem 44PPS

Expression for the amount of time that each van has spent on the road after an additional $t$ minutes is $A_1=20+t$ and $A_2=35+t$

Explanation of Solution

Given information: The first Ski club van has been on the road for $20$ minutes, and the second van has been on the road for $35$ minutes

Calculation:

Let the additional time be $t$

Given that the first Ski club van has been on the road for $20$ minutes.

Expression for the amount of time that first van has spent on the road after an additional $t$ minutes is given as

  $A_1=20+t$

Also, given that the second van has been on the road for $35$ minutes

Thus, Expression for the amount of time that second van has spent on the road after an additional $t$ minutes is given as

  $A_2=35+t$

Conclusion:

Hence, Expression for the amount of time that each van has spent on the road after an additional $t$ minutes is $A_1=20+t$ and $A_2=35+t$

(a)

To determine

To calculate: To write the ratio for the first van’s time on the road to the second van’s time on the road and use long division to rewrite the ratio as an expression

Answer to Problem 44PPS

Ratio for the first van’s time on the road to the second van’s time on the road is $\frac{t+20}{t+35}$

Explanation of Solution

Given information: The first Ski club van has been on the road for $20$ minutes, and the second van has been on the road for $35$ minutes

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Calculation:

Ratio for the first van’s time on the road to the second van’s time on the road is given as follows:

  $\frac{t+20}{t+35}$

Dividing the expression with the divisor to derive the quotient and remainder:

  $t+35\begin{array}{c}\hfill 1\\ \hfill \overline{)\begin{array}{l}t+20\\ t+35\\ --\\ ----\\ -15\end{array}}\end{array}$

Thus, expression is

  $\begin{array}{l}\Rightarrow 1+\frac{-15}{t+35}\\ \Rightarrow 1-\frac{15}{t+35}\end{array}$

Conclusion:

Hence, expression for ratio is $1-\frac{15}{t+35}$