Question

I was walking to the store at the same time as my friend Angela. No matter what, She has always gotten there twice as fast as me. Half way to the store her friend picks her up on his scooter which was 10 times faster than me. She got there in 30 minutes. How long did it take for me to get there?

Answer 1

Let's call your speed "a"

her walking speed is then "2a"

and her friend's scooter speed is 10 a

let's also call the distance you need to walk "d"

so the time (t)you need is:

d/t=a
t=d/a

and her time is:
 t=$\frac{d}{2} /2a+ \frac{d}{2} /10a$
(half a distance with the speed of 2a and half a distance (d/2) with the distance of 10 a

now we count (we know that her time is 30 minutes)

30= $\frac{d}{4a}+\frac{d}{20a}$ //multiply by 20a

600a= $5d+d$
600a=6d/divide by 6
100a=d

Now, in order to calculate your time we need to calculate:

t=d/a

but we know how much is d now!
t=$\frac{100a}{a}$=100

which means that you need 100 minutes, or 1 h 40 minutes!!!