Question regarding Manhattan challenge problem

[sreekanth.ramayanam]

Edwin is planning to drive from Boston to New Orleans. By what percent would his travel time be reduced if Edwin decides to split the driving time equally with his friend George, instead of making the trip alone?

(1) The driving distance from Boston to New Orleans is 1500 miles.

(2) George’s driving speed is 1.5 times Edwin’s driving speed.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements together are sufficient, but NEITHER statement alone is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


I agree to you that answer is B but achieving exact value for % seems to be wrong

Given in B G = 1.5 E

Scenario 1 : it takes E = d/t1 and therefore t1 = d/E.
Scenario 2: d/2 distance travelled @ speed E and d/2 travelled at speed G
total time t2 = d/2/E + d/2/G = d/2[1/E + 1/G] = d/2 [1/E + 1/1.5E] = d/2E[1+2/3]

t2/t1 = 1/2[1+2/3] = 5/6
Therefore our answer is 1-t2/t1 = 1-5/6 = 1/6 * 100 ---> 17%. Where as you gave it as 20%.

Just wanted to know if i am missing something. i know this is data sufficiency but wanted to make sure underlying concept is same.

[esledge]

They decided to split the travel time not the travel distance.

I just made up some smart numbers to check the 20% figure:

Edwin:
Rate = 10 mph (made up)
Time = t (same as George's driving time)
Distance = 10t

George:
Rate = 15 mph (1.5 times the rate I made up for Edwin)
Time = t (same as Edwin's driving time)
Distance = 15t

Total:
Distance = 150 miles (made up)
Time = Edwin's driving time + George's driving time = 2t.

If Edwin made the trip alone, t = d/r = 150 miles / 10 mph = 15 hours.

If they travel together,
Total Distance = 150 miles = 10t + 15t = 25t.
Therefore, t = 150/25 = 6 hours, and Total time = 12 hours.

Thus, the trip together is 3 hours shorter than the 15 hours it would take Edwin alone. 3/15 = 1/5 = 20%.