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Puzzling math problem (for me anyway)

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Puzzling math problem (for me anyway)

by bdevas01 » Mon Feb 15, 2010 3:29 pm
I'd like to hear how you would solve this one:

Gloria leaves home for school on a bicycle at 12 mph. 20 minutes later, her mother sees Gloria's English paper on her bed and leaves to bring it to her. If her mother drives at 36 mph, how far must she drive before she reaches Gloria?

Also, according to the answer sheet, the correct equation to solve it is 12x = 36(x - 1/3), but I keep getting 2 when I solve that, and 2 does not satisfy the equation.

What is the right way to solve this and what am I doing wrong?

Thanks
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by Brent@GMATPrepNow » Mon Feb 15, 2010 4:35 pm
bdevas01 wrote:I'd like to hear how you would solve this one:

Gloria leaves home for school on a bicycle at 12 mph. 20 minutes later, her mother sees Gloria's English paper on her bed and leaves to bring it to her. If her mother drives at 36 mph, how far must she drive before she reaches Gloria?

Also, according to the answer sheet, the correct equation to solve it is 12x = 36(x - 1/3), but I keep getting 2 when I solve that, and 2 does not satisfy the equation.

What is the right way to solve this and what am I doing wrong?
Thanks
Here's one solution.
Aside: Don't forget that distance = rate x time

Begin by recognizing that, when Mother reaches Gloria, they will have both travelled the same distance.
In other words: Total distance travelled by Mother = Total distance travelled by Gloria
Let t be the amount of time the Mother drove
Total distance travelled by Mother = 36t

In the first 20 minutes (1/3 hours), Gloria travelled 4 miles (12 mph x 1/3 hours)
After that, she rode her bike for t hours (t is the amount of time her mother drove and, during that time, Gloria was riding her bike). During those t hours, Gloria travelled 12t miles
So, Total distance travelled by Gloria = 4 + 12t

So, Total distance travelled by Mother = Total distance travelled by Gloria
36t = 4 + 12t

Solve for t to get t = 1/6 hours
If Mother travelled 1/6 hours at a speed of 36 mph, then she travelled a total of 6 miles (1/6 x 36 = 6)
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by bdevas01 » Mon Feb 15, 2010 5:05 pm
Thank you!

Makes perfect sense now.
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by Stuart@KaplanGMAT » Mon Feb 15, 2010 6:03 pm
bdevas01 wrote:I'd like to hear how you would solve this one:

Gloria leaves home for school on a bicycle at 12 mph. 20 minutes later, her mother sees Gloria's English paper on her bed and leaves to bring it to her. If her mother drives at 36 mph, how far must she drive before she reaches Gloria?

Also, according to the answer sheet, the correct equation to solve it is 12x = 36(x - 1/3), but I keep getting 2 when I solve that, and 2 does not satisfy the equation.

What is the right way to solve this and what am I doing wrong?

Thanks
Here's another way you can solve this type of question:

first, there's a key rule to remember:

when two objects are moving in the same direction, SUBTRACT their rates to get their relative rate.

Now let's reason it through:

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

D = r * t = 12 * 1/3 = 4

So, when mom leaves home, she's 4 miles behind Gloria.

Relative rate = mom's rate - gloria's rate = 36 - 12 = 24mph

So, d=4 and r=24:

t = d/r = 4/24 = 1/6

1/6 of an hour = 10 minutes (sadly, you didn't post choices, so no clue which of those matches - in the future, please always include the answers and the source!).
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by harsh.champ » Mon Feb 15, 2010 10:57 pm
Stuart Kovinsky wrote:
bdevas01 wrote:I'd like to hear how you would solve this one:

Gloria leaves home for school on a bicycle at 12 mph. 20 minutes later, her mother sees Gloria's English paper on her bed and leaves to bring it to her. If her mother drives at 36 mph, how far must she drive before she reaches Gloria?

Also, according to the answer sheet, the correct equation to solve it is 12x = 36(x - 1/3), but I keep getting 2 when I solve that, and 2 does not satisfy the equation.

What is the right way to solve this and what am I doing wrong?

Thanks
Here's another way you can solve this type of question:

first, there's a key rule to remember:

when two objects are moving in the same direction, SUBTRACT their rates to get their relative rate.

Now let's reason it through:

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

D = r * t = 12 * 1/3 = 4

So, when mom leaves home, she's 4 miles behind Gloria.

Relative rate = mom's rate - gloria's rate = 36 - 12 = 24mph

So, d=4 and r=24:

t = d/r = 4/24 = 1/6

1/6 of an hour = 10 minutes (sadly, you didn't post choices, so no clue which of those matches - in the future, please always include the answers and the source!).
I am with Stuart on this one.Solving using the concept of relative speed helps reduce 2 to 3 equations and even the calculation becomes less cumbersome.

Hey bdevas01,
Also, according to the answer sheet, the correct equation to solve it is 12x = 36(x - 1/3), but I keep getting 2 when I solve that, and 2 does not satisfy the equation.
I wanted to ask what is "x" in the above equation.I guess you mistook "x" as the wrong variable and put it as the answer.Maybe x is replacing some other variable "lets say y" and y is the answer.

Also,can you post the answer choices also.That can help you also and the ppl solving the ques. as we can also use the elimination technique .
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by amittilak » Tue Feb 16, 2010 12:06 pm
This is a good question for rates.
Here's how I solved:
R*T=D
Gloria travels for 20 mins @ 12mph
D = 12*20/60 = 4 miles, Which means the distance between her mother and Gloria is 4 miles.
Now, the mother's speed is 36 mph, which means that she is catching up to Gloria @ 36 - 12 = 24 mph
Time in minutes for the mother to catch up with Gloria, is 24 * t = 4
t = 4/24 = 1/6 * 60 = 10 minutes (in addition to the previous 20 minutes Gloria was travelling)
Thus, the total distance travelled by Gloria in 30 minutes is (20 + 10) * 12/60 = 6 miles
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by shashank.ism » Wed Feb 17, 2010 11:51 am
bdevas01 wrote:I'd like to hear how you would solve this one:

Gloria leaves home for school on a bicycle at 12 mph. 20 minutes later, her mother sees Gloria's English paper on her bed and leaves to bring it to her. If her mother drives at 36 mph, how far must she drive before she reaches Gloria?

Also, according to the answer sheet, the correct equation to solve it is 12x = 36(x - 1/3), but I keep getting 2 when I solve that, and 2 does not satisfy the equation.

What is the right way to solve this and what am I doing wrong?

Thanks
Let T hrs be the time (from the point when gloria leaves home) after they meets...so distance covered by Gloria= 12T miles
Distance covered by her mother = 36(T-1/3)miles
12T = 36(T-1/3) ---> T= 3T-1 --> T=1/2 hr
so distance covered = 12x(1/2) = [spoiler]6 miles
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