During a trip, Yogi Bear traveled 62.5% of the total distance at an

The fastest way is to assume x = 1 and then see which of the options satisfy this.

Average speed = \(\frac{d}{\frac{0.625}{40}+\frac{0.375}{x}}\)= 2.56.

Only option C gives this value and is thus the correct answer.

I prefer to take Numbers in Such questions to make the expressions simpler

e.g. Let Distance = 1000
i.e. 62.5% of Distance = 625

Average Speed = Total Distance / Total Time

Total Distance Covered = 1000

Total Time = Time taken to cover 625 miles @40 miles/hr +Time taken to cover (1000-625) = 375 miles @x miles/hr

Total Time = (625/40)+(375/x)

i.e. Average Speed = 1000/ [(625/40)+(375/x)] = \(\frac{{320x}}{{5x+120}}\)

Answer: Option C

The easiest way would be to chose 40mph for the rest of the trip, but this leaves you with option C and E. On the test day I would probably go with the 50/50 chance because of the time.

Similar question to practice: during-a-trip-francine-traveled-x-percent-of-the-total-94933.html

Why are you not reducing 320x/5x+120 to 64x/x+24? My teacher would have marked this wrong.

You are correct and it's a good habit to have . Whenever you want to report an answer in fractions, you should be reducing both the numerator and denominator. But if the options do not have anything reduced, then you do not have to. You can not challenge the options provided and you have to play within the confines of the question statement and the options provided.

got 40x/0.625x+15 after multiplying by 8/8 get = 320x/5x+120

C

I find it somehow strange that the answer choice is not written is the most simplified form!!!


62.5% can be rewritten as 5/8

so we have 5d/8 - distance, and 40 mph - speed.
we then have = 3d/8 - distance, and x mph - speed.

to find the average speed, we need to find the total time.

time for first leg: 5d/8 * 1/40 = d/64
time for second leg: 3d/8 * 1/x = 3d/8x

total time: d/64 + 3d/8 | multiply first by x, second by 8.
(xd+24d)/64x
factor d in the numerator:
d(x+24)/64x
is the total time.
total distance = d.

to find the average speed, divide distance by time.

d*64x / d(x+24)

simplify by D

64x/(x+24).
right away, we can eliminate B and D.
let's multiply what we have by 5.
320x/(5x+120).

still don't get why the answer wouldn't be in the most simplified way.

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