Question

Jim began a 200 mile bike trip to build up stamina for a triathlete competition. Unfortunately, his bike chain broke, so he finished the trip walking. The whole trip took 8 hours. If Jim walks at a rate of 3 miles per hour and rides at 35 miles per hour, find the amount of time he spent on the bicycle

Answer 1

That is a simple question to solve.

First, let's consider the whole trip = 8 hours. If, between this 8 hours, we have x hours travelled by bicycle and y hours travelled on foot, we have:

$\text{wholetrip}_{\text{hours}}=\text{bicycle}_{\text{hours}}+\text{walking}_{\text{hours}}$

Once:

$\begin{gathered} \text{wholetrip}_{\text{hours}}=8\text{ hours} \\ \text{bicycle}_{\text{hours}}=\frac{x}{\text{bicycle}_{\text{miles}/h}} \\ \text{walking}_{\text{hours}}=\frac{(200-x)}{\text{walking}_{\text{miles}/h}} \end{gathered}$

So, we have:

$\begin{gathered} 8_{}=\frac{x}{35}_{}+\frac{(200-x)}{3} \\ 8_{}=\frac{3x+7000-35x}{105} \\ 840-7000=3x-35x \\ x=\frac{6160}{32} \\ x=192.5miles \end{gathered}$

Where x is the number of miles spent by bicycle.

Now, for y (number of miles spent walking) we have:

$\begin{gathered} y=200-192.5 \\ y=7.5miles \end{gathered}$

Now we can calculate the amount of time spent walking and on the bicycle as follows:

$\begin{gathered} \text{walking}_{\text{hours}}=\frac{(200-192.5)}{3} \\ \text{walking}_{\text{hours}}=2.5h \end{gathered}$

and,

$\begin{gathered} \text{bicycle}_{\text{hours}}=\frac{192.5}{35} \\ \text{bicycle}_{\text{hours}}=5.5h \end{gathered}$

So, the final answer is: Jim spent 5.5 hours on the bicycle.