John and Jacob set out together on bicycle traveling at 15

[JoJo]

hi,

can someone please explain this? thx.

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)
3
3 1/3 (this is the correct answer)
3 1/2
4
4 1/2

[Harish Dorai]

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.

[GMAT 2007]

Jojo,

John and Jacob started at 15 m/h & 12 m/h respectively.

After 40 min. John travelled 15*2/3 = 10 miles and Jacob travelled 12*2/3 = 12*2/3 = 8 miles

When John stopped he was 2 miles ahead of Jacob. Now it took john 1 hr to fix the bike, So in one hr Jacob travelled 12 more miles, which makes him 10 miles ahead of John.

Now assume John takes time 't' to catch Jacob, So the following equations holds

(10 + x)/15 = x/12 where x = distance travelled by jacob when john resumed

solving above x = 40 miles.

It means John has to travel 50 miles to catch Jacob and it would take him 50/15 = 10/3 = 3 1/3 hrs

Hence (B) is the answer

Hope it helps

GMAT 2007

[preetchilled]

Jojo,

John and Jacob started at 15 m/h & 12 m/h respectively.

After 40 min. John travelled 15*2/3 = 10 miles and Jacob travelled 12*2/3 = 12*2/3 = 8 miles

When John stopped he was 2 miles ahead of Jacob. Now it took john 1 hr to fix the bike, So in one hr Jacob travelled 12 more miles, which makes him 10 miles ahead of John.

Now assume John takes time 't' to catch Jacob, So the following equations holds

(10 + x)/15 = x/12 where x = distance travelled by jacob when john resumed

solving above x = 40 miles.

It means John has to travel 50 miles to catch Jacob and it would take him 50/15 = 10/3 = 3 1/3 hrs

Hence (B) is the answer

Hope it helps

GMAT 2007

Hi Stacey: i thought original GMAT questions were not allowed to be put up as per the GMAC guidelines...would you care to look it up or please ignore and apologies in advance from my end if i am wrong.

Thanks Preet

[mschwrtz]

Hey Preet,

1) How do you know that this is an actual GMAT question? I don't recognize it. If you can confirm that it is from a banned source, we'll certainly delete it.

2) On the other hand, it doesn't seem to be one of ours, either, so it is in the wrong forum. I'll move it.

[alexia]

I multiplied Jacob's rate by 100/60 to get 20 miles, then subtracted by the distance John had already travelled to get ten miles, the distance John needed to catch up to Jacob.

I then subtracted their rates to get a relative rate of 3m/h for closing the ten mile gap between the two, which gave me the answer of t =10/3 or 3 1/3, the correct answer.

My question is, did I get the right answer in the wrong way?

Thanks.

[RonPurewal]

I multiplied Jacob's rate by 100/60 to get 20 miles, then subtracted by the distance John had already travelled to get ten miles, the distance John needed to catch up to Jacob.

I then subtracted their rates to get a relative rate of 3m/h for closing the ten mile gap between the two, which gave me the answer of t =10/3 or 3 1/3, the correct answer.

My question is, did I get the right answer in the wrong way?

Thanks.

Nope. Flawless.

The more methods you can devise, the better.