vipulgoyal wrote:OA [spoiler]25%[/spoiler]
let the total distance = 120
speed of j = 30 , K = 60
j stops when k trevelled 25% distance means 30, it means oth J and K travelled half an hour before J stops
J travelled 15 , hence K travelled 105 ----------- 1
now the case when j would not have been stopped, let they meet at x distance from J
x/30 = 120-x/60, x= 40, it means K travelled 120-40 = 80
now time differance 105/60 - 80/60 = .4
.4/1.75(105/60)= approx 25%
Hi!
Picking numbers is a great way to approach this question. However, you got a bit lost partway through your solution.
Let's go back a few steps!
First, let's state our task: We need to solve for the % greater Karen runs with gimpy John than with healthy John. In other words, percent change. So, we're solving for:
(Karen longer time - Karen shorter time)/(Karen shorter time) * 100%
We're told that Karen runs 50% faster than John - but 60 isn't 50% more than 30, it's 100% more (i.e. your numbers didn't actually match the info in the Q stem). So, let's set John's rate at 20 and Karen's rate at 30.
Now that we've chosen rates, let's pick a distance that works well with those rates. We know that John is going to stop after 25% of the distance, so let's pick a number that, when divided by 4, will be easily divisible by 20. 80 looks like a good fit.
Now that we finally have our numbers (spending a bit of extra time picking manageable numbers almost always saves you even more down in the long run), let's solve!
Total distance = 80
John only runs 25%, which is 20. At 20mph, John runs for 1 hour.
Karen runs the remaining 60. At 30mph, Karen runs for 2 hours. Hey, numbers are working out nicely so far!
Now we need to figure out how long Karen would have run if John hadn't pulled up lame. When solving for time of two objects moving TOWARD each other, we ADD their rates:
total time = (total distance)/(sum of rates)
t = (80)/(50) = 8/5
So, if John hadn't stopped, each would have run for 8/5 hours.
Finally, we plug into the originally noted formula:
changing 2hours to 10/5 hours, we get:
(10/5 - 8/5)/(8/5)
= (2/5)/(8/5)
= 2/8
= 25%
Pick (A)!
One important note: the question doesn't say
approximately what percent, so the answer will be exact. Since you didn't end up with an exact match for one of the choices, you should have known that there was a mistake somewhere in your methodology.
