DS: M travelled X miles/hr the 1st y miles & 1.25X the

[Guest]

M travelled X miles/hr the 1st y miles & 1.25X for the last 40-y miles. The time M took to travel 40 miles was what % of the time taken her if travelled at an average of X miles for the entire trip?

A: X=48
B: y=20

Ans: B

Xt=y and 1.25Xt=40-y.
Therefore 1.25Xt=40-Xt ....0.25Xt=40.....Xt=160.......t=160/X

Entire trip at X: Xt=40
Therefore time = 40/X divided by 160/x = 25% (Hence my confusion: why is the answer B - why not None?!)

where am i going wrong here?...
thanks

[Guest]

ok - see that i made mistake above of equating t=t, since times not equal.

but even if assign t+1 to the rate of X miles/hr (since would take longer) and just assign t to the 1.25X miles/hr,
the eqns become;

Xt +X =y ....and
1.25Xt= 40-(Xt+X)
1.25Xt +Xt = 40-X
2.25Xt=40-x

so the answer should be statement A (which provides the value of X).

so why is the answer B? (which gives the value of Y, which isn't apparently necessary to solve the question).

[RonPurewal]

M travelled X miles/hr the 1st y miles & 1.25X for the last 40-y miles. The time M took to travel 40 miles was what % of the time taken her if travelled at an average of X miles for the entire trip?

A: X=48
B: y=20

you can't use t and t + 1, because you don't know that there is a one-hour difference between the times. (that '1' would have to be a literal '1': i.e., it would have to stand for 1 hour.)
rhetorical question: are you in the 9-session class? if so, did you mistakenly assume that the 't' and 't + 1' from the rate problem in session 5 apply to all time differentials? they don't: the '1' in that problem specifically comes from the one-hour time difference between the two parts.

(1) only:
insufficient, because you don't know the lengths of time for which M traveled at the two different speeds.
consider the extreme cases:
if y is 0.0001 or so, then M traveled at 1.25x = 60 mph for virtually the whole trip. therefore, her time will be very close to 80% of what it would have been at x = 48 mph.
if y is 39.999 or so, then M traveled at 48 mph for virtually the whole trip. therefore, her time will be very close to 100% of what it would have been at x = 48 mph.

(2) only:
if y = 20, then M traveled 20 miles at 1.25x mph and the other 20 miles at x mph.
solve d = rt for time: t = d/r. therefore, the total time is 20/(1.25x) + 20/x = 16/x + 20/x = 36/x hours.
the time she'd have taken at a constant speed of x mph is 48/x hours.
we know that the percentage difference can be calculated:
(36/x) / (48/x) = 36/48 = 75%
(notice that there's no need to actually calculate this, unless you don't otherwise see that the x's cancel)
sufficient

ans = b