Question

Marco drove from home to work at an average speed of 50 miles per hour and returned home along the same route at an average speed of 46 miles per hour if his total driving time for the trip was four hours how many minutes did it take Marco to drive from work to home

Answer 1

125 minutes

Step-by-step explanation:

Let's call x, the number of hours that Marco drove from home to work and y the number of hours that Marco drove from work to home.

The total time is 4 hours, so we can write the following equation:

x + y = 4

Additionally, the distance from home to work and from work to home is the same, so using the speed, we can write the following equation:

50x = 46y

Where 50x is the distance in miles from home to work and 46y is the distance in miles from work to home.

Now, we can solve for x in the first equation:

`\begin{gathered} x+y=4 \\ x=4-y \end{gathered}`

Replacing it on the second equation a solving for y, we get:

`\begin{gathered} 50(4-y)=46y \\ 50\cdot4-50\cdot y=46y \\ 200-50y=46y \\ 200=46y+50y \\ 200=96y \\ (200)/(96)=y \\ (25)/(12)=y \end{gathered}`

It means that Marco drove 25/12 hours from work to home. Now, we need to write those hours in minutes, so:

`(25)/(12)\text{hour}\cdot\frac{60\text{ minutes}}{1\text{ hour}}=(25\cdot60)/(12)\text{ minutes = 125 minutes}`

So, Marco drive from work to home 125 minutes