Jim has arrived late for his golf tee time with his friends.

Question

Jim has arrived late for his golf tee time with his friends. When he arrives at the course, he discovers that his friends have already walked 180 yards ahead on the course and that they are continuing to walk forward at a rate of 1.5 yards per second. A bystander with a golf cart takes pity on Jim and drives him to meet his friends at the rate of 4 yards per second. Once Jim meets his friends, he exits the cart and walks with them at their rate for the next 120 yards. What is Jim’s approximate average speed for his total trip?

1.8 yards per second
2.0 yards per second
2.4 yards per second
2.7 yards per second
3.0 yards per second

A. 1.8 yards per second
B. 2.0 yards per second
C. 2.4 yards per second
D. 2.7 yards per second
E. 3.0 yards per second

This is a question from a Kaplan diagnostics test (free online). 
1) How long can you solve this for? 
2) How do you approach this type of questions?
3) Can you point me to other similar distance problems?

Bunuel · Accepted Answer

Jim's rate: 4 yards per second; Friends' rate: 1.5 yards per second; Their relative rate: 4-1.5=2.5 yards per second. To cover the distance of 180 yards between them \frac{180}{2.5}=72 seconds are needed. Distance covered by Jim is 4*72=288 yards. To cover the next 120 yards Jim will need \frac{120}{1.5}=80 seconds. Average \ rate=\frac{total \ distance}{total \ time}=\frac{288+120}{72+80}\approx{2.7} . Answer: D. DS questions on Distance/Rate: search.php?search_id=tag&tag_id=44 PS questions on Distance/Rate: search.php?search_id=tag&tag_id=64 Hope it helps.

cyberjadugar · Answer

Hi,

The question involves the concept of relative speed and average speed,
To find the average speed, we have to find the total distance traveled and the total time taken:

Jim covers the total trip in two parts:
  Part 1  : Travelling on cart @ 4 yards/sec
Time taken by Jim to meet his friends =  \frac {distance}{rel. speed}  =  \frac{180}{4-1.5} 
= 72 sec
Distance traveled = 4*72 = 288 yards
  Part 2  : Jim travels 120 yards @ 1.5 yards/sec
time taken =  \frac {120}{1.5}  = 80 secs

Total distance travelled = 288 + 120 = 408
Total time taken = 72 + 80 = 152
Thus, average speed =  \frac {408}{152}  = 2.68 ~ 2.7 yards/sec

Answer (D)

It took me 2 minutes to solve & 10 mins to write here.

Regards,

stoy4o · Answer

Thank you guys.

Bunnel, I'll take a look at your links. 
I appreciate it.

lemonhalls · Answer

can someone explain why relative speed is used here, ie 4 - 1.5 to get 2.5 yard per s

Kris01 · Answer

When Jim arrives he finds that his friends are 180 yards ahead of him and are still walking at a rate of 1.5 yards/sec. However, he gets a ride in a golf cart and is able to travel at a speed of 4 yards/sec. During this time, his friends are still walking at a speed of 1.5 yards/sec. Thus, the distance between them will get reduced at a rate of 4-1.5=2.5 yards/sec. The time taken to cover the distance of 180 yards is effectively increased and hence we use the relative speed to calculate the time.

Consider this situation for example. You are walking with your friend when suddenly you meet someone and stop to talk to the person. Meanwhile your friend continues walking. After you end the conversation, you run to catch up with your friend. However, your friend continues to walk. Wouldn't this increase the time taken to reach your friend as opposed to the time taken if he waited for you when you start running? What is the reason for this increase in time? This is because even though you are running, your friend is also walking in the same direction and thus the distance between you is reducing at a slower rate than it would if he waited for you. Thus, you need to calculate the relative speed to account for this.

Hope this helps! However, if you have any further concerns, please let me know.

KarishmaB · Answer

The concept used here is relative speed. When two objects move in the same direction, one going faster than the other, the speed of the one going faster relative to the one going slower is the difference of the speeds. Check out this post I wrote sometime back on relative speed to get a hang of the basic concept. The answer explanation will make a lot of sense thereafter. https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/07 ... elatively/

sauravleo123 · Answer

Hi karishma,
I understand the concept of relative speed. However cant we solve this question with the approach outlined below??

The time when jim travels the 180 miles in cart is 45 seconds i.e. 180/4. In these 45 seconds his freinds travel a further 1.5*45 miles. So jim has to travel a total of 180+67.5 miles at a speed of 4 yards/mile to meet his friends. But by using this approach i am getting the answer as 2.59 approx. What am i missing.

KarishmaB · Answer

What happens in the time that Jim travels the 67.5 yards? During that time, his friends go further ahead at the speed of 1.5 yards/s and he still doesn't catch up with them. 
Time taken by Jim to cover 67.5 yards is 67.5/4 = 16.875 secs
So the friends have traveled another 1.5*16.875 yards

So it is best to use the relative speed concept. Jim has to cover 180 yards (relatively) at a relative speed of 4 - 1.5 = 2.5 yards/sec. Think of it like this: Out of his speed of 4 yards/sec, he uses 1.5 yards/sec to cover whatever distance his friends are covering now and the rest 2.5 yards/sec he uses to cover the gap of 180 yards between them. 
Time taken by Jim to meet his friends = 180/2.5 = 72 secs
Time for which he travels at 1.5 yards/sec = 120/1.5 = 80 secs

Average speed will be close to the middle of 1.5 and 4 but closer to 1.5 (using weighted averages). Middle of 1.5 and 4 is 2.75 so it will be 2.7 yards/sec

sauravleo123 · Answer

Now i understand. Thank you so much karishma. Your explanations are the best I have encountered on this forum.

kusena · Answer

Given Jim's friends has a lead of 180 yards and moving at 1.5 yards/sec speed
Jim on golf cart with speed 4 yards/sec has to meet this friends, assuming he meets them after "t" secs

So the total distance traveled by Jim and his friends should be same so as to meet them=> 180+1.5t=4t
=> 180=2.5t
=>72secs, so Jim meets his friends after traveling 72 secs at 4 yards/sec speed---First part of his journey (288 yards in 72 secs)
Now, Jim travels 120 yards with speed 1.5 yards/sec in 120/1.5=80 secs---second part of his journey (120 yards in 80 secs)

So avg speed of Jim= total distance traveled/ total time
=> (288+120)/(72+80)=408/152
=>2.7 yards/sec approx
Ans D..hope its clear

jlgdr · Answer

Very nice question. Similar to Manhattan's GMAT 'Moving walkway' Let's get this started First, relative rate 4-1.5=2.5 yards per second to catch up with his buddies Therefore, time will be 180/2.5 =360/5=72 seconds Now in 72 seconds he traveled= 72*4 = 288 yards Now, he will travel the next 120 yards in = 120/1.5 = 240/3 in 80 seconds Hence average speed will be 288+120 / 80+ 72 = 2.7 Answer is D Kudos if it helps Cheers! J

gracie · Answer

d=distance walked by J's friends from 180 yards to where J overtakes them
(180+d)/4=d/1.5
d=108
total distance for J=180+108+120=408 yards
total time for J=(180+108)/4+120/1.5=152 seconds
408/152=2.7 yards per second average speed

NagrajB · Answer

Average Speed = Total Distance / Total Time

Distance 1 = 180
Distamce 2 = 120

Time 1 = 180/Relative Speed of Jim = 180/(4 - 1.5) = 180/2.5 = 72
Time 2 = 120/Speed of Group = 120/1.5 = 80
Total Distance = 300 Yards
Total Time = 80+72 = 152 seconds
Hence Average Speed apprx 2 / second

My 2 cents on problem solving
Introduce numbers as late as possible into the calculation
Solve it in equation format, use cancellation of terms etc

gracie · Answer

let d=distance from 180 yards to point where J meets friends
(180+d)/d=4/1.5
d=108 yds
108+180+120=408 total yds
(180+108)/4 yps=72 sec
120/1.5 yps=80 sec
72+80=152 total seconds
408 total yds/152 total sec≈2.7 yps average speed for total trip
D

Akshit03 · Answer

Hi, Please help me with where i'm thinking wrong.
When he is covering the 180 yards that he is behind at 4 yards/second, his friends would not have stopped. In that time they would move some distance ahead, so he has to cover 180 yards + extra distance moved.
Why have we not considered that?
I'm really confused.

ScottTargetTestPrep · Answer

Let’s let t = the time, in seconds, that Jim is in the golf cart. During these t seconds, he travels 4t yards. His friends have already walked 180 yards, plus 1.5t additional yards while Jim is in the golf cart catching up to them. Thus, we have:.

4t = 1.5t + 180

2.5t = 180

t = 72 seconds

We know that Jim travels 4 x 72 = 288 yards in 72 seconds while he is in the golf cart.

Next, let’s determine the time he walks with his friends after he catches up with them:

120/1.5 = 80 seconds

So his total distance is 4 x 72 + 120 = 408 yards, and his total time is 72 + 80 = 152 seconds. Therefore, his average speed for the entire trip is:

408/152 ≈ 2.7 yards per second

Answer: D

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Jim has arrived late for his golf tee time with his friends.

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