Question

Link can ride his bike 20 miles into a 3 mph headwind in the same amount of time he can ride 30 miles with a 3 mph tailwind. What is Link’s biking speed?

Short answer

The speed of the bike is 15 mph.

Step-by-step solution

Given information

The covered distances are given in the direction of the wind and against the direction of the wind.

Form the rational equation

Use the given statement to form the required rational expression.

• Assume that the speed of the bike is $v$then the rate of the bike in the direction of the wind is v+3 whereas the speed of the bike against the wind is v-3.
• Use the speed formula $time\mathit{=}\frac{\mathit{d}\mathit{i}\mathit{s}\mathit{tan}\mathit{c}\mathit{e}}{\mathit{s}\mathit{p}\mathit{e}\mathit{e}\mathit{d}}$to write the expression for the time.

$\begin{array}{rcl}Tim{e}_{Inthedirectionofwind}& =& \frac{30}{v+3}\\ Tim{e}_{againstthewind}& =& \frac{20}{v-3}\end{array}$

As the time in both the cases is the same hence make both the obtained expression equal to each other to find the required equation.

Solve the equation to find the speed

Apply the algebraic operations to find the speed of the bike.

• Use the cross multiplication to solve the obtained equation to find the value of v.

$\begin{array}{rcl}\frac{30}{v+3}& =& \frac{20}{v-3}\\ 30(v-3)& =& 20(v+3)\\ 30v-90& =& 20v+60\\ 30v-20v& =& 90+60\\ 10v& =& 150\\ v& =& \frac{150}{10}\\ v& =& 15mph\end{array}$