10. Eddie and his sister walked from home to school. His sister started walking at 8.00 am at an average speed of 50 m/min. Eddie started walking at 8.05 am at a speed of 60 m/min. Eddie caught up with his sister at mid-point between the school and his home. Find the distance between Eddie's home and the school.

His sister started walking at 8.00 am at an average speed of 50 m/min. Eddie started walking at 8.05 am at a speed of 60 m/min. Eddie caught up with his sister at mid-point between the school and his home.

Let the distance between school and home is x.

Let t is the time taken by Eddie sister to reach at mid-point between school and home.

Eddie caught up with his sister at mid-point between the school and his home.

That means his sister covers x/2 distance.

[tex]Time=\frac{Distance}{Speed}[/tex]

Speed of Eddie sister is 50 m/min.

[tex]t=\frac{\frac{x}{2}}{50}[/tex] .....(1)

Eddie started walking at 8.05 am at a speed of 60 m/min.

[tex]t-5=\frac{\frac{x}{2}}{60}[/tex]

[tex]t=\frac{\frac{x}{2}}{60}+5[/tex] .....(1)

Equate both the equation as shown:

[tex]\frac{\frac{x}{2}}{50}=\frac{\frac{x}{2}}{60}+5[/tex]

[tex]\frac{x}{100}=\frac{x}{120}+5[/tex]

[tex]\frac{x}{100}-\frac{x}{120}=5[/tex]

[tex]\frac{12x-10x}{1200}=5[/tex]

[tex]2x=6000[/tex]

[tex]x=3000[/tex]

Hence, the distance between Eddie's home and the school is 3000 m