At 1:00, Jack starts to bicycle along a 60 mile road at a constant spe

Question

At 1:00, Jack starts to bicycle along a 60 mile road at a constant speed of 15 miles per hour. Thirty minutes earlier, Scott started bicycling towards Jack on the same road at a constant speed of 12 miles per hour. At what time will they meet?

A. 1:30
B. 3:00
C. 5:00
D. 6:00
E. 9:00

Kudos for a correct solution.

A. 1:30
B. 3:00
C. 5:00
D. 6:00
E. 9:00

EMPOWERgmatRichC · Accepted Answer

Hi All,

This is an example of the 'Combined Rate' question; on Test Day, they're relatively rare (you'll probably see just 1) and they're usually written in a way that requires a certain amount of real "math" work to get to the correct answer.

By using the answer choices in this question, you can actually AVOID most of the work though.

In the first sentence, we know Jack's starting time (1pm), speed (15 mph) and distance (60 miles), so we can quickly figure out how long it would take Jack to travel the entire distance (4 hours). This tells us that, at 5pm, Jack would be at the other end of the road. We know that Scott is cycling TOWARDS him though, so some time BEFORE 5PM, they'll meet. Eliminate Answers C, D and E.

With the remaining two answers, 1:30pm is much TOO early to be the meeting time. Neither Jack nor Scott is traveling fast enough to meet up that early. Eliminate A. There's only one answer left..

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

Aektann · Answer

let x be time.

15x+12(x+1/2)=60;
27x=54;
x=2;

=>

1:00 + 2 hr = 3:00

LaxAvenger · Answer

13:30 Scott 12m 
14:30 Scott 24m
15:30 Scott 36m -> 15:00 Scott 36 - 6m = 30m

14:00 Jack 15m
15:00 Jack 30m

Answer B

chetan2u · Answer

IN THESE QUESTIONS WE FIND THE DISTANCE BETWEEN TWO WHEN BOTH ARE MOVING AND THEN FIND THE TIME IT TAKES THE FASTER ONE TO COVER THAT DISTANCE...
Scott has already moved for half an hour so he is 12/2 miles ahead.. =6 miles 
jack covers 3 miles extra each hour when compared to scott...
so he will cover 6 miles in 6/3=2 hours..
2 hours after 1:00 is 3:00...ans B

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: B

Explanation: Solution: B The relevant formula is Rate x Time = Distance. If Jack's time is t, then Scott's time is t + .5, since he started one-half hour earlier. Jack's distance is therefore 15t, and Scott's distance is 12 (t + .5). The sum of their distances will be the distance apart that they started. Therefore we can say that 15t + 12 (t + .5) = 60. This simplifies to 15t + 12t + 6 = 60, which means that 27t = 54, and t = 2. Since Jack left at 1:00, and his time was t, he met Scott at 3:00.

PareshGmat · Answer

Answer = B = 3:00

At 01:00, Scott has already travelled 6 kms, so remaining distance = 60-4 = 54

Say Jack meets Scott at "x" kms from his own starting point

\frac{x}{15} = \frac{54-x}{12}

x = 30

Time required by Jack to travel 30kms = 2 Hrs

They will meet at 03:00

laddaboy · Answer

Given : Distance is 60 miles

Scott has a 30 mins lead and hence covers 6 miles.

So when Jack starts he and Scott have to cover a distance of 54miles ( 60-6) to reach each other, with a speed of 27 miles/hour ( 15+12 ) => 2 Hours,

1:00 + 2 hours = 3:00...

kanusha · Answer

Scott has already moved for half an hour so he is 12/2 miles ahead.. =6 miles 
jack covers 3 miles extra each hour when compared to scott...
so he will cover 6 miles in 6/3=2 hours..
2 hours after 1:00 is 3:00...ans B

Joeyjoe · Answer

Scott is ahead by  30min x 12 miles per 60 min = 6 miles.

Find the relative speed of Jack to Scott,  15 miles/hr - 12 miles/hr = 3 miles/hr

For Jack to catch up and meet Scott is  6 / 3 = 2 hrs

1:00 + 2 hrs = 3:00 = Answer

gvvsnraju@1 · Answer

Distance Traveled by Jockey = 6 + Distance Traveled by Scott
Lets Say they will meet after T hours.
15T = 12T + 6
T=2 Hours
therefore, They Will meet @ 03:00 pm

Nunuboy1994 · Answer

12(x + 1/2) +15x =60
 27x =54 
 x=2

2 hours from 1 or 
2 hours and 30 mins from 12 :30

B

ScottTargetTestPrep · Answer

Solution:
 
We can let t = the time, in hours, Jack takes to catch up and meet Scott, and create the equation:

15t = 12(t + 1/2)

15t = 12t + 6

3t = 6

t = 2

Therefore, it takes 2 hours for Jack to catch up and meet Scott. Since he starts at 1:00, he meets Scott at 3:00.

Answer: B

TheNightKing · Answer

Scott has a lead of 6 miles because he travels for 30 minutes at 12mph. So Jack has to catch up 6 miles.

Now the different between the speeds of Jack and Scott is 3mph. So assuming both travel at their constant speed it will take 2 hours for jack to catch up with Scott. Since Jack starts at 1:00 they will meet at 3:00.

Answer B

e3thekid · Answer

Since Jack and Scott are traveling towards each other, this is a converging type of rate question. The overall distance between them is 60 miles, as is mentioned in the question stem. It is also mentioned that Scott started traveling toward Jack 30 mins earlier.

Jack Distance = 15 * t 
Scott Distance= 12 *(t + 0.5)

Jack Distance + Scott Distance = Total Distance

15t + 12t + 6 = 60
27t = 54 
 t = 2

They will meet in t = 2 hours

We can add t = 2 to Jack’s start time of 1 pm.

1 pm + 2 hours = 3 pm

Option B

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bumpbot · Answer

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At 1:00, Jack starts to bicycle along a 60 mile road at a constant spe

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