GWD-22-2滔滔

Q2:In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour.  She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take.  Was her estimate within 0.5 hour of the actual time that the trip took?

(1)
                Joan’s estimate for the distance was within 5 miles of the actual distance. бS?-5,5] ,б 表示路程S的估计偏差

(2)             Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed. бV?-10,10] 

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.
                бT?-1/2,1/2]

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

answer E,我觉得C，解题如灰色部分

you can not just divide the boundary like divide 5 with 10

in fact, we have:

S=s+ds V=v+dv

T=S/V=(s+ds)/(v+dv)

the capital letters represent actual value and the small letters represent the estimated value.

T can be expressed as a Tayor Series: T=(s/v-sdv/v²)+(ds/v-dsdv/v²)+o(ds)²+o(dv)²

=(t-sdv/v²)+(ds/v-dsdv/v²)+o(ds)²+o(dv)²

thus, there is no a simple relationship between T and t.