Kevin drove from A to B at a constant speed of 60 mph. Once he reache

Question

Kevin drove from A to B at a constant speed of 60 mph. Once he reached B, he turned right around with pause, and returned to A at a constant speed of 80 mph. Exactly 4 hours before the end of his trip, he was still approaching B, only 15 miles away from it. What is the distance between A and B?

A. 275 mi
B. 300 mi
C. 320 mi
D. 350 mi
E. 390 mi

Kudos for a correct solution.

A. 275 mi 
B. 300 mi 
C. 320 mi 
D. 350 mi 
E. 390 mi

EgmatQuantExpert · Accepted Answer

Hi  arkle ,

The question statement tells us   "exactly 4 hours before the end of his trip he was  still approaching B , only 15 miles away from it"  . Since he was approaching B, that would mean Kevin was on his way from A to B. We know that he drove from A to B at a constant speed of 60 miles/hour.

Using Distance = Speed * Time

15 = 60 * T i.e. T =  \frac{1}{4}  hours = 15 minutes.

Using this information,we can then easily calculate his journey time from B to A i.e. (4 -  \frac{1}{4} ) hours = 3.75 hours.

Since we know Kevin's speed from B to A which is 80 miles/hour, we can calculate the Distance = 80 * 3.75 = 300 miles between A & B.

Hope its clear!

Regards
Harsh

shriramvelamuri · Answer

Usually I flunk Time and Distance problem; but, this was seemed a bit achievable.

My thought process is equate Time in all respects.

Let the distance be X.

From A-> B= X/60

From B-A= X/80

Overall Time for the trip= X/60+X/80

Substract 4 from above (4 ago he was 15 miles away from B)

X/60+X/80 -4.

Time taken to cover x-15= x-15/60

X/60+x/80 -4= X-15/60

Solve equation, you will be get answer= X= 300miles.

Hope this is clear.

mehrdadtaheri92 · Answer

This is a straightforward problem if we carefully consider the concept of rate / time problems type. and answer is indeed , B

so, here we go , the driver went from point A to B in the CONSTANT speed of 60 mph , the simple concept here is , 60 mph / 60 min =1 it means to cover every mile

, the driver has to spend one minute , so keep it in the mind,

Next : the problem says that Exactly 4 hours before the end of the trip , drive was 15 miles away point B and approaching to the point B , it means , 4 hours was the time to cover

15 miles to cover 15 miles toward the point B and also cover the distance from reverse direction from point B to the point A . already we know that 15 miles with the constant speed of 60 mph

, takes 15 minutes to cover , so if we deduct 15 minutes form 4 hours , we can get the time required to get from point B to the point A WITH 80 mph.

so , we have : 4 hours - 15 minutes = 3 hours and 45 minutes

here we have time required to travel from point B to point A , and we are given the rate of travel 80 mph , so we can get the distance between point B to the point A ,

3.45 h = 3 hours and 45 minutes , 80 mph for 3 hours is : 80 *3 =240 miles and 45 minutes = 45/60 = 3/4 hours then , 80 * 3/4 = 60 miles

so, Total distance = 240+ 60 = 300 miles..... ANSWER : B

regards,

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

In the last 15 miles of his approach to B, Kevin was traveling at 60 mph, so he traveled that distance in ¼ hr, or 15 minutes. That means, when he arrived at B, 15 minutes had elapsed, and he took (4 hr) – (15 min) = 3.75 hr to drive the distance D at 80 mph. It will be easier to leave that time in the form (4 hr) – (15 min).

D = RT = (80 mph)  = 320 mi – 20 mi = 300 mi

Answer = (B)

PareshGmat · Answer

Answer = B =300

Refer distance diagram below:

Attachment:

pse.png [ 2.97 KiB | Viewed 28613 times ]

Say the distance between A & B = d

Given that

Time required for 15 miles (From A to B) + Break (x minutes) + Time required for d miles (from B to A) = 4 hours (Shown in double line in the diagram)

\(\frac{15}{60} + x + \frac{d}{80} = 4\)

x = Time consumed pausing/breaking at point B. This is already included in 4 hours. Equation setup showing prominence of x.

\(d = \frac{15}{4} * 80 = 300\)

arkle · Answer

How did we reach to this?

In the last 15 miles of his approach to B, Kevin was traveling at 60 mph, so he traveled that distance in ¼ hr, or 15 minutes.

ThxQ

adiagr · Answer

Travelling.JPG Refer attached diagram. Entire distance that Kevin has to cover is in blue line. The diagram clarifies the exact location of "15 miles". When Kevin was approaching B, his speed was 60 mph. Time taken by Kevin in covering those 15 miles, before he touched B: = (1/4) hours. (Note: In order to cover the entire distance shown in the diagram, Kevin takes 4 hours) His trip would end when he reaches back A. So (entire time taken from travelling back from B to A) + (1/4) hrs = 4 hours Time taken in return journey from B to A = 4 - (1/4) = 3 hours + (3/4) hours Speed: 80 Mph 80 * 3 + 80 * (3/4) = 240 +60 = 300 Km. Answer: B.

ShashankDave · Answer

mikemcgarry  
shouldn't the question say "without pause"? Because if there is a pause, then without knowing for how much time he paused, we can't find the distance

mikemcgarry · Answer

Dear ShashankDave , Yes, that's a typo. Apparently it wasn't copied correctly from the source. I made the correction to the problem at the top of the thread. Thank you for pointing this out. Mike

ScottTargetTestPrep · Answer

Let the distance between A and B = d. Therefore, the time from A to B is d/60 and the time from B to A is d/80, and thus the total time for the round trip is d/60 + d/80 = 4d/240 + 3d/240 = 7d/240. Since we are given that exactly 4 hours before the end of his trip, he was still approaching B (and was thus still traveling at 60 mph), only 15 miles away from it, we can create the equation:

60(7d/240 - 4) = d - 15

7d/4 - 240 = d - 15

7d - 960 = 4d - 60

3d = 900

d = 300

Alternate Solution:

Let’s concentrate only on the 4-hour time period. During this time, he was still going from A to B at a rate of 60 mph (or 1 mile per minute), and he traveled 15 miles to actually get to B. Thus, he traveled 15 miles in 15 minutes. This means that the remaining 3 hours and 45 minutes of the 4-hour travel time was all used to get from B back to A. During these 3.75 hours, he traveled at a rate of 80 mph; thus, the distance from B to A = 3.75 x 80 = 300 miles.

Answer: B

fskilnik · Answer

? = d\,\,\,\left

Excellent opportunity to use UNITS CONTROL, one of the most powerful tools of our course!

\left  = \frac{{\left }}{{\left }}

From "Exactly 4 hours before the end of his trip, he was still approaching B, only 15 miles away from it. " we have (see image attached):

4 = {T_{{	ext{CB}}}} + {T_{{	ext{BC}}}} + {T_{{	ext{CA}}}} = \frac{{15}}{{60}} + \frac{{15}}{{80}} + \frac{{d - 15}}{{80}} = \frac{{1 \cdot \boxed{20}}}{{4 \cdot \boxed{20}}} + \frac{d}{{4 \cdot 20}} = \frac{{d + 20}}{{80}}\,\,\,\,\,\,\,\,\,\,\,\,\,\left

\frac{{d + 20}}{{80}} = 4\,\,\,\, \Rightarrow \,\,\,\,\,? = d = 4 \cdot 80 - 20 = 300\,\,\,\,\,\left

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Dereno · Answer

GIVEN  Kevin 🧍‍♂️ drove from A to B at 60 mph. Once KEVIN reached B , he turned back immediately to A at a speed of 80 mph.

QUESTION STEM  -  Exactly 4 hours before the end of his trip, he was still approaching B, only 15 miles away from it.
    Couple of things to note here   
1. Kevin is approaching B - if Kevin approaches B , he is driving at speed 60 mph. 
2. Exactly 4 hrs before 
3. 15 miles away from it .  That’s B. Now, at 60 mph he takes 15 mins to cross 15 miles.

Now,  he has  exhausted 15 mins  in this 4 hrs, leaving him  3 hr 45 mins to reach A from B at 80 mph.

distance travelled T 80 mph for 3 hr 45 min is 240+ 80*(45/60) =  300 miles . Option B

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Kevin drove from A to B at a constant speed of 60 mph. Once he reache

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