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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.

Sagot :

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 :

[tex]\begin{gathered} \text{ Sp}eed=\frac{Dis\tan ce}{Time} \\ \text{Then, }Time=\frac{Dis\tan ce}{Spped} \end{gathered}[/tex]

Then using these expression

Time taken by the brother is :

[tex]\begin{gathered} \text{ Time taken by brother =}\frac{x}{60} \\ \text{Time taken by the sister=}\frac{y}{55} \end{gathered}[/tex]

As total time is 11 hours so:

[tex]\frac{x}{60}+\frac{y}{55}=11[/tex]

So we get the two set of equation :

[tex]\begin{gathered} \frac{x}{60}+\frac{y}{55}=11 \\ x+y=635 \end{gathered}[/tex]

Simplify the set of equation :

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

[tex]\begin{gathered} \frac{x}{60}+\frac{y}{55}=11 \\ \frac{x}{60}=11-\frac{y}{55} \\ x=660-\frac{12y}{11} \\ \text{Susbtitute the value of x in the second equation:} \\ x+y=635 \\ 660-\frac{12}{11}y+y=635 \\ \frac{-12}{11}y+y=635-660 \\ \frac{-12y+11y}{11}=-25 \\ \frac{-1}{11}y=-25 \\ y=25\times11 \\ y=275 \end{gathered}[/tex]

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

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