Question

Your brother and sister took turns driving on a 635 mile trip that took 11 hours to complete. your brother drove at a constant speed of 60 miles per hour and your sister drove at a constant speed of 55 miles per hour. let x be the number of miles your brother drove and y be the number of miles your sister drove. find the number of miles each of your siblings drove.

Answer 1

Your brother and sister took turns driving on a 635 mile trip

Total distance travel on trip = 635

Let x be the disatnce travel by your borther and y be the miles travel by the sister

SO, x + y = 635

It took 11 hours to complete the trip

Speed of brother = 60 miles per hour

Speed of sister = 55 miles per hour

The general expression for the speed is :

`\begin{gathered} \text{ Sp}eed=(Dis\tan ce)/(Time) \\ \text{Then, }Time=(Dis\tan ce)/(Spped) \end{gathered}`

Then using these expression

Time taken by the brother is :

`\begin{gathered} \text{ Time taken by brother =}(x)/(60) \\ \text{Time taken by the sister=}(y)/(55) \end{gathered}`

As total time is 11 hours so:

`(x)/(60)+(y)/(55)=11`

So we get the two set of equation :

`\begin{gathered} (x)/(60)+(y)/(55)=11 \\ x+y=635 \end{gathered}`

Simplify the set of equation :

Simplify the first equation for x and then put it into another :

`\begin{gathered} (x)/(60)+(y)/(55)=11 \\ (x)/(60)=11-(y)/(55) \\ x=660-(12y)/(11) \\ \text{Susbtitute the value of x in the second equation:} \\ x+y=635 \\ 660-(12)/(11)y+y=635 \\ (-12)/(11)y+y=635-660 \\ (-12y+11y)/(11)=-25 \\ (-1)/(11)y=-25 \\ y=25*11 \\ y=275 \end{gathered}`

Substitute y = 275 in the first equation :

x + y = 635

x + 275 = 635

x = 360

As x represent the distance travel by the bother and the rest by sister

Distance travel by brother is 360 miles and the distance travel by the sister is 275 miles

Answer : x = 360 miles, y = 275 miles