John and Jacob set out together on bicycle traveling at 15 and 12 mile

Question

John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2

Show Answer

Official Answer

B

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2

swanidhi · Accepted Answer

John's speed - 15 miles/hr
Jacob's speed - 12 miles/hr

After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 12x5/3 = 20 miles.

Now, when John starts riding back, the distance between them is 10 miles. Jacob and John are moving in the same direction.  For John to catch Jacob, the effective relative speed will be 15-12 = 3 miles/hr.

Thus, to cover 10 miles at 3 miles/hr, John will take 10/3 = 3 1/3 hours

Answer B

PareshGmat · Answer

Distance travelled by John in 40 Minutes \(= \frac{15}{60} * 40 = 10\) Miles (At this point, his car gets punctured)

Distance travelled by Jacob in 40 Minutes\(= \frac{12}{60}* 40 = 8\)Miles (He is still moving)

John is idle for 1hr, means he's still at 10 Miles from initial start

Jacob is still moving for 1hr, means he has travelled another 12 Miles; total distance travelled from initial start = 12+8 = 20 Miles

Relative distance between Jacob & John = 10 Miles

Refer diagram below:

Attachment:

meet.png [ 3.37 KiB | Viewed 51374 times ]

Time taken by John to reach the meeting point would be same as time taken by Jacod

Setting up the equation

\(\frac{10+x}{15} = \frac{x}{12}\)

x = 40

Total catch up time taken \(= \frac{10+40}{15} = \frac{31}{3} Hrs\)

Answer = B

manpreetsingh86 · Answer

distance travelled by john in 40 minutes = 15(40/60) = 10 km
distance travelled by jacob in 40 minutes = 12(40/60) =8 km 
after 40 minutes john leads jacob by 2 km.
after 40 minutes jacob continues to ride for 1 hour, while john stops to fix a flat tire. during this time jacob covers 12km. but since initially john was leading the jacob by 2km thus, distance now between john and jacob =12-2 =10km

thus time taken by john to catch up with jacob = 10/(15-12)
=3 1/3

hence B

LighthousePrep · Answer

I agree with Paresh. Just wanted to make a slight modification since it looks like there is a typo in the last line:

Total catch up time taken  = \frac{10+40}{15} = 3\frac{1}{3}  Hrs

Poorvasha · Answer

John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

A. 3
B. 3 1/3
C. 3 1/2
D. 4
E. 4 1/2

Show Answer

Official Answer

B

At 1 hour and 40 minutes (time at which John resumes after his 1 hour halt) = John's distance covered is 15*40/60 = 10 miles and distance covered by Jacob is 20 (12*40/60+12).

Difference in their speeds = 3
Time that will be taken to catch up = difference in distances / differences in speeds = (20-10)/3 = 10/3 (B)

BigM · Answer

10 miles and distance covered by Jacob is 20 (12*40/60+12). Why do you add +12 here?

lynnglenda · Answer

Johns Travel: 
40 minutes  15  mph + 1 hour time to fix tire + Catch up time  15  mph (Let us assume it as T) 
Distance travelled before catch up = Distance traveled in 40 min + 0(when fixing the tire) + Distance traveled during catch up time T which is equal to: 
15mph x 2/3 hr( 2/3 hr = 40 mins) + 0 + 15 mph x T

Jacobs Travel: 
40 minutes  12  mph + 1 hour time  12  mph + T minutes  12  mph 
ie. Distance travelled by Jacob = 12 x 2/3 + 12 x 1 + 12 x T.

When John catches up Jacob, both would have traveled the same distance.

So the above calculations for John and Jacob can be converted to an equation.

15 x 2/3 + 0 + 15T = 12 x 2/3 + 12 x 1 + 12T 
10 + 15T = 20 + 12T 
3T = 10

T = 10/3 which 3 1/3 hours.

So time taken to catch up is 3 1/3 hours.

Louis14 · Answer

How is it that the time taken by Jacob would be the same as time taken by John?

davidbeckham · Answer

Hi  Bunuel , after 40 mins John has covered 10 miles and Jacob has covered 8. After 1 hour, John is still on 10 and Jacob is on 20 but is still moving - so why should that not be considered while calculating the answer? John should cover the distance of 10 miles in 40 minutes and Jacob would cover 8 more miles in this time - so shouldn't John be covering 18 miles in total to catch up with Jacob?

rishab0507 · Answer

Hi, trying to answer your query,
Your part reasoning is correct, but not in later part.
After 1 hour, John is still on 10 and Jacob is on 20 but is still moving - :  Correct 
so shouldn't John be covering 18 miles in total to catch up with Jacob? :  incorrect

For catch and chase questions ,important thing is relative speed. Hoping you know that if both move in same direction speeds are deducted :
So relative speed is : 15-12 = 3.
Now in these questions, its eas when you think the object in lead as stationery and the former catching it . If you keep calculating the 1st ran how much in time required to catch. it will make things difficult. So, moving on,
Speed : 3 kmph
Distance travelled by john in 1.40 hours : 10
Distance travelled by jacub in 1.40 hours : (100/60 )*12 =20

distance left to be covered : 10 : Now if you see i am not considering Jakub is still travelling and keeping him stationery at 20 will make this easier.
Time : D/T : 10/3 or 3 1/3

Hope you understood this catch.

athudi1507 · Answer

Bunuel 
how this is solved with this equation in last 10 + x / 15 = x / 12
how to solve with this approach and not relative speed approach
plz explain in detail
thanks in advance

luisdicampo · Answer

Deconstructing the Question  
The problem has three distinct phases because John and Jacob travel at different speeds from the very beginning.

John's Speed:  15 mph  
 Jacob's Speed:  12 mph  
 Phase 1: Both move for 40 mins (2/3 hour). 
 Phase 2: John stops for 1 hour; Jacob continues.

Step 1: Analyze Phase 1 (The first 40 mins)  
They start together but separate immediately.
 Distance_John = 15 * 2/3 = 10 miles 
 Distance_Jacob = 12 * 2/3 = 8 miles 
At this point, John is at mile 10 and stops. Jacob is at mile 8 and keeps going.

Step 2: Analyze Phase 2 (The 1-hour Stop)  
John stays at mile 10.
Jacob travels for 1 hour at 12 mph.
 Distance_Jacob_New = 8 + 12 = 20 miles

Now calculate the  Real Gap  when John restarts:
 Gap = Jacob_Pos - John_Pos 
 Gap = 20 - 10 = 10 miles

Step 3: Calculate Catch-up Time  
John chases Jacob with a relative speed of  15 - 12 = 3 mph .
 Time = Gap / Relative_Speed 
 Time = 10 / 3 hours 
 Time = 3 1/3 hours

Answer:  B

John and Jacob set out together on bicycle traveling at 15 and 12 mile

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John and Jacob set out together on bicycle traveling at 15 and 12 mile

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