Question

Ben usually walks frome to school, and returns on a bike. It takes him 40 minutes altogether. One day he biked from home to the school and back, which took him 32 minutes. How much time will it take him if he walks from home to school and back?

Answer 1

48 minutes

1) We can solve this problem using a Linear System of Equations. Let's call walk "w" and bike by "b

2)So we can set the following system, considering the given data:

`\mleft\{\begin{matrix}w+b=40 \\ 2b=32\end{matrix}\mright.`

Thus, let's solve it by the Substitution Method. Let's solve the II equation for b:

`\begin{gathered} 2b=32 \\ (2b)/(2)=(32)/(2) \\ b=16 \end{gathered}`

2.2)We can plug that into the first equation and then find how long did it take to go walking to school:

`\begin{gathered} w+b=40 \\ w+16=40 \\ w+16-16=40-16 \\ w=24 \end{gathered}`

Notice that the question wants to know how long does it take to go to school walking home to school and back, so we can write out:

`2w=2\cdot(24)=48`

3) Hence, Ben would take 48 minutes to go walking home to school and back