mejia401 wrote:

During a trip, Yogi Bear traveled 62.5% of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of \(x\) miles per hour. In terms of \(x\), what was Yogi Bear's average speed for the entire trip?

A. \(\frac{{320x}}{{3+200x}}\)

B. \(\frac{{x+80}}{{120x}}\)

C. \(\frac{{320x}}{{5x+120}}\)

D. \(\frac{{320x+5}}{{200x}}\)

E. \(\frac{{120x}}{{x+80}}\)

Again, from

OG 13 with different conditions.

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.