d=r*t (simple distance formula)
d = distance
r = rate/speed
t = time

question is asking you when will d of gloria = d of mother.

d of gloria = d of mother =>
r of gloria * t of gloria = r of mother * t of mother =>
12 * t = 36 (t - 1/3)

time is in hours since our rate/speed is in per hour. Therefore 20 min = 1/3 of 1 hour, so you subtract that from gloria's time to get the mother's time.

galit_d2d wrote:hi, I saw a problem in the math review document which is published in this forum.

gloria leaves home for school, riding her bicycle at the rate of 12mph 20 min later after she leaves her mother sees gloria's eng paper on her bed and leaves to bring it to her. If her mother drives at 36mph how far must she drives before she reaches gloria?

there is no answer just an equation which is:
12x= 36(x-1/3)
when :
x=time of gloria
x-1/3=time of the mother

I don't understand this...
somebody..help...

This is a classic GMAT "catch up" question.

To answer this question, we want to do two things:

(1) figure out where the 1st person is when the 2nd person starts moving; and

(2) SUBTRACT their rates to find out how quickly the 2nd person is catching up.

Here:

Gloria has been traveling for 1/3 of an hour at 12mph.

Catch up distance = r*t = 12 * 1/3 = 4 miles

Catch up rate = Mom's rate - Gloria's rate = 36 - 12 = 24mph

So, the question becomes:

"How long does it take to travel 4 miles at 24mph?"

time = distance/rate = 4/24 = 1/6 of an hour = 10 minutes.

I forgot to mention that after you solve for t (total travel time for gloria), you'll get 30 min.

The question asks how far must the mother drive, so you need to take the time the mother drives (30 min - 20 min = 10 min = 1/6 hr) multiplied by her speed (36 mph) which will give you 6 miles.

thank you I understood both ways:)