# Reiny! Reiny! Reiny!

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1. Oanh walked from her home to the grocery store at 3 mi/h and jogged home at 6 mi/h. Her total round trip was 15 minutes (1/4h). How far from Oanh's home is the grocery store? (use an equation to solve this)

Help, I am totally clueless on this.

• Reiny! Reiny! Reiny! -

let her time walking be t hours
then the distance she walked = 3t miles

let her time jogging back home be 1/4 - t hours
so the distance she jogged = 6(1/4 - t)

but aren't those two distances the same ?

so...
3t = 6(1/4 - t)

I am sure you can solve this for t, then sub that value back into 3t to get the distance.

• Reiny! Reiny! Reiny! -

Wait, I don't get it.

I solved
3t = 6 (1/4 - t)
and got 11.66666666666....

and then what do I do?
..or did I do that wrong?

• Reiny! Reiny! Reiny! -

3t = 6 (1/4 - t)
3t = 3/2 - 6t
9t = 3/2
t = 3/18 = 1/6

then 3t, which was the distance
= 3(1/6) = 1/2

so the distance is 1/2 mile

check:
time walking = 1/2 ÷ 3 = 1/6 hour
time jogging = 1/2 ÷ 6 = 1/12 hour

1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 hour

• Reiny! Reiny! Reiny! -

Oh, i see.

thank you.

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