Question

Josh is training for the Olympics. He canswim 8 mph freestyle and 6 mph butterfly. Ifhe swims the same distance doing eachstroke and it takes him 3.5 hours total, howfar did he swim?

Answer 1

Taking x and y as the number of hours Josh swims each style, we have that:

`x+y=3.5`

We also know that he swins the same distance doing each style, it means that the product of 8 times x equals the product of 6 times y (the product of the speed times the time is the distance):

`8x=6y`

Use this equation to write one of the variables in terms of the other variable:

`\begin{gathered} x=(6y)/(8) \\ x=(3)/(4)y \end{gathered}`

Now, use this expression in the first equation, write it in terms of the same variable (y) and solve:

`\begin{gathered} (3)/(4)y+y=3.5 \\ (7)/(4)y=3.5 \\ 7y=3.5\cdot4 \\ y=(14)/(7) \\ y=2 \end{gathered}`

Using this value, we can find x:

`\begin{gathered} x=(3)/(4)y \\ x=(3)/(4)(2) \\ x=1.5 \end{gathered}`

Use these values to find the distance swum doing each style and then add the distances:

`\begin{gathered} 8x=8\cdot1.5=12 \\ 6y=6\cdot2=12 \\ 12+12=24 \end{gathered}`

He swam 24 meters.