What is the distance between Harry's Home & Office?

[krisburg]

This question was in a CAT II exam:

Data sufficiency

What is the distance between Harry's home and office?

(1) Harry's average speed on his commute to work this Monday was 30 mph

(2) If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

- I understand why A,B & D are the wrong answers, but I don't understand why the answer is "C." In the explanation (from the CAT exam) it said that we can discern from statement #2 that the trip takes 30 minutes. How is this possible if we aren't given a base time (duration) for how long the commute is?

[Kweku.Amoako]

let d = distance between home & ofice r = speed t = time

then d = r x t

so we need the product of speed & time

(1) r = 30
substituting back in the equation we get

d = 30 x t not sufficient

(2) d = (2r)(t-15)
d = 2rt - 30r Not sufficient since we have no values for r,t or rt

(3) r = 30 and d = 2rt - 30r

we also know that d = rt ...at this point the 3 equations should be sufficient to solve for d,r,t but to demonstrate:

since d = rt we can substitute in the equation d = 2rt - 30r

there d = 2(d) -30r ..solving this gives you d = 30r
we also know that r = 30 so substituting this in d = 30r gives us d = (30) (30) ...sufficient

[Ben Ku]

Nice explanation, Kweku.

Krisburg:

Code: Select All Code

In the explanation (from the CAT exam) it said that we can discern from statement #2 that the trip takes 30 minutes. How is this possible if we aren't given a base time (duration) for how long the commute is?

Because rate * time = distance, then rate and time are inversely related. What that means is that if you travel at twice the rate, you will arrive there in half the time.

As an illustration, suppose we are traveling 120 miles at a rate of 30 mph. This will take us 4 hours. If we travel the same 120 miles at twice the speed, or 60 mph, it will take half the time, or 2 hours.

Hope that makes sense!