Question

Jim began a 156 mile bike trip to build up stamina . Unfortunately his bike chain broke so he finished walking. Th whole trip took 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 33 miles per hour find the amount he spent on the bike.

Answer 1

This diagram represents the problem

We know that distance = speed*time; D=S*t

Total distance: 156 miles

time: 6 h

Speed1: 33 miles/h

Speed2: 5 miles/h

for interval 1:

`\begin{gathered} D_1=S_1\cdot t_1 \\ D_1=33\cdot t_1 \end{gathered}`

for interval 2:

`\begin{gathered} D_2=S_2\cdot t_2 \\ D_2_{}=5\cdot t_2 \end{gathered}`

for the whole trip: -Eq 1. Distance

`\begin{gathered} D=D_1+D_2 \\ D=33\cdot t_1+5\cdot t_2 \\ 156=33\cdot t_1+5\cdot t_2 \end{gathered}`

and also: -Eq 2. Time

`\begin{gathered} t=t_1+t_2 \\ 6=t_1+t_2 \end{gathered}`

Now we have a system of 2 equations with 2 unknowns.

Let's solve it!

`\begin{gathered} 156=33t_1+5t_2 \\ t_1=(156-53t_2)/(33) \\ (156-5t_2)/(33)+t_2=6 \\ t_2=(3)/(2) \\ t_1=(156-5\cdot(3)/(2))/(33) \\ t_1=(9)/(2) \end{gathered}`

We can see that he spent 4.5 hours riding the bike and 1.5 h walking