Johnny travels a total of one hour to and from school. On the way ther

Question

Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?

A. 2 miles
B. 4 miles
C. 4.8 miles
D. 8 miles
E. 10 miles

Kudos for a correct solution.

A. 2 miles
B. 4 miles
C. 4.8 miles
D. 8 miles
E. 10 miles

SOURH7WK · Answer

Answer: B) 4 miles.

Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*5*20/(5+20) = 8m/hr
the distance between school & home should be half of that. ie. 4 miles

D3N0 · Answer

Ans: B

let the distance between Home and School is S
Solution: total time taken = time jog +time bus
= 1 = s/5 + s/20
= 5s/20=1
s=4 miles

mejia401 · Answer

Backsolved, with a 5th of an hour is 12 minutes.
A. if the route took him  24  minutes running there, it will take less than that to return home, and therefore  2  miles is incorrect.
B.  4*12=48  and 4 miles going  20 mph takes  12  minutes, for  4 miles is  \frac{1}{5} th of  20 miles, or it takes  \frac{1}{5} hours to travel  4 miles going  20 mph. Anyhow, 48+12=60. Thus, B is correct.

IMO B.

lipsi18 · Answer

t1+t2=1;
t1= d/5, t2=d/20; d= distance;
1= d/5+d/20 = 5d/20 =>d=4

Hence answer is B

KS15 · Answer

Let one way distance be =d
Now, d/5+d/20=1
5d/20=1
d=4 miles
Answer B

shailendra79s · Answer

Distance = d
Time taken while walking = t
=> d = 5 x t => t = d/5 ......(1)
For the return journey
Distance = d
Time taken = 1-t
=> d = 20 x (1-t) ....(2)
Calculating (1) & (2) for d
Distance d = 4 miles (B)

Mo2men · Answer

Spotting a the ratio between 2 speeds 20/5=4. The time should be divided by same ratio 20/5=48/12

d= 20 * 12/60= 4 or 5* 48/60 = 4mile
answer B

VenoMfTw · Answer

IMO :: B

Given
 S_1  = 5
 S_2  = 20
Distance is constant

Since distance is constant we can say that   speed is inversely proportional to time

Thus

\frac{S_1}{S_2}  =  \frac{T_2}{T_1}

Thus  \frac{T_2}{T_1}  =  \frac{1}{4}

Thus  T_1  = 4/5 of total time
Distance =  S_1  *  T_1 
= 4 miles

noTh1ng · Answer

HI, whats the logic here? Why is the distance half the average speed?

bdawg2057 · Answer

i solved using Rate * Time = Distance

Going: Rate (5 mph) * Time (x) = Distance

Coming Rate (20mph) * Time (1-x) = Same Distance

5x=20-20x;
25x=20
x=4/5

5 * 4/5 = 4

SOURH7WK · Answer

First I calculated the avg speed ie 8m/hr. In the question it was mentioned that he travelled for 1 hr to and fro. That means he travelled 8m to and fro. So the distance one way should be 4m.

Bunuel · Answer

PRINCETON REVIEW OFFICIAL SOLUTION:

What is the question asking?

The question is looking for a distance that Johnny travels. Good news for us. All the answer choices are in miles.

Where are you starting?

I have two rates of travel and a total time to apportion to and from the school. Let me suggest that there are many ways to attack this one. I will offer just a few to demonstrate that multiple methods lead to the same spot.

A) The Algebra Student says: I will work with the rates and I can see that one is four times the other in terms of time, because D=R*T (Distance = Rate X Time). I know they are inversely related. So 5T= 1 hour. Therefore T=.2 hours. I can take either the bus speed or the bicycle speed and plug in: 20 miles an hour multiplied by .2 hours results in 4 miles. We check the work and we are right.

B) The Plug-In Master says, let me try each of the distances and see what I get. So he starts at 4.8 miles and divides that by 4 miles per hour and recognizes that he is already over an hour time, tries 4 miles and the math works.

C) The Class Math Wiz tells us that there is an elegant way to take the reciprocal of the rates, add them together, flip that result over and voilá we get 4 miles. While our Wiz is absolutely correct, we all shake our heads and look for something that we all can use.

D) Finally, our Class Ball Parker says that all of this was unnecessary, because we only had an hour available to us for both jogging and the bus. Since this is true, we exclude answers C, D, and E. They are too big. We look at 2 miles and realize it is too small and won’t even come close to totaling one hour and without any math, arrive at the exact same answer.

I guarantee that there are even more ways to attack this one problem. Which method is the best? There really is no answer to that. As a student taking the GMAT you really have to determine for yourself which method works for you. However, the first step is to understand where you are starting and where you are going. You need to know exactly what you are looking for, and what tools and information you have available to help you get to the answer.

This is why it is crucial to work as many problems in your practice tests as possible. The more familiar you are, both with the math and the way in which the questions are presented, the better the chances for success.

abhishekdadarwal2009 · Answer

Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?

A. 2 miles
B. 4 miles
C. 4.8 miles
D. 8 miles
E. 10 miles

Kudos for a correct solution.

A. 2 miles
B. 4 miles
C. 4.8 miles
D. 8 miles
E. 10 miles

total time=1 hour

total time=time from home to school + time from school to home.

we know that distance is same in both cases so we assume distance to be D

D/5+D/20=1

or 5D/20=1

or D=20/5=4.

Option B:4 miles is correct.

ScottTargetTestPrep · Answer

We can create the following equation since we know that time = distance/rate and since the total time is 1 hour. We can also let d = the distance from home to school.

d/5 + d/20 = 1

4d/20 + d/20 = 1

5d/20 = 1

5d = 20

d = 4

Answer: B

bumpbot · Answer

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Johnny travels a total of one hour to and from school. On the way ther

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