Question

My sister can walk from school to home in 35 minutes. I can walk from school to home in 20 minutes. But today I stayed for some extra help, and my sister was already 3/7 of the way home when I started. If I walk at my usual speed, can I catch my sister before she gets home? Explain your reasoning.

Answer 1

Answer:

you both will reach the home at the same time.

I) You can catch your sister.

ii) Reason: you both will reach home at the same time.

Step-by-step explanation:

Let "d" be distance from school to home.

Let's find the speed of you and your sister.

Speed = $\frac{Distance}{Time}$

Your speed = $\frac{d}{20}$

Your sister's speed =  $\frac{d}{35}$

Today, You stayed for some extra help by the time your sister covered $\frac{3}{7}$ of the way home.

Remaining distance to reach the home = $1 - \frac{3}{7}d = \frac{7-3}{7}d = \frac{4}{7}d$

=

Now let's find the time to be taken your sister to reach the home.

Time = $\frac{distance}{speed}$

= $\frac{\frac{4}{7}d }{\frac{1}{35} d} = \frac{4}{7} *\frac{35}{1} = 20$

So, your sister will take 20 minutes to get home by the time your start.

We know that it takes you 20 minutes to reach your home.

Therefore, you both will reach the home at the same time.

I) You can catch your sister.

ii) Reason: you both will reach home at the same time.