Points A, B, and C lie, in that order, on a straight railroa

Question

Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 100 miles per hour and the train's average speed when traveling from point B to point C was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?

A. 80
B. 85
C. 87.5
D. 90
E. 275/3

A. 80
B. 85
C. 87.5
D. 90
E. 275/3

Bunuel · Accepted Answer

The distance from point A to point B is twice the distance from point B to point C: AB=2 units and BC=1 unit (distances);

Average rate = (total distance)/(total time) -->  rate=\frac{2+1}{\frac{2}{100}+\frac{1}{75}}=\frac{3}{\frac{1}{30}}=90 .

Answer: D.

fortsill · Answer

S=d/t
=3x/( 2x/100 + x/75 )
= 90. D.

Bunuel · Answer

Though your approach is correct. You don't really need to use a variable here, you can just take any two numbers in a ratio 2:1, 2 and 1 for example. Or even better 100 and 50 to make calculation easier:  rate=\frac{100+50}{\frac{100}{100}+\frac{50}{75}}=\frac{150}{1+\frac{2}{3}}=\frac{150}{\frac{5}{3}}=90 .

fortsill · Answer

Thanks bunuel...I agree variable x wasn't needed and in such cases I use it knowing that eventually it'll cancel out...

Bunuel · Answer

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Baracuda123 · Answer

A to B = 200 miles  (plugged in number) 
B to C = 100 miles  (plugged in number)

Since A to B speed is 100 mph, then the ride took 2 hours. Since B to C speed is 75 mph, the ride took 1+1\3 hours which is 80 minutes.

Thus, overall time was 3 hours and 20 minutes. Total distance is 300 miles. So Distance = rate * time, then rate = distance\time

( Just keep in mind that we have to convert minutes into hours so 200 minutes = 3+1\3 or 10\3 )

To wrap up, 300\(10\3)=90  (D)

WholeLottaLove · Answer

Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 100 miles per hour and the train's average speed when traveling from point B to point C was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?

A. 80
B. 85
C. 87.5
D. 90
E. 275/3

Average speed = distance/time

Because we are looking for average speed we can pick a distance for the variable d.

Total length = 450.
Speed A-B = 100
Speed B-C = 75
Average Speed = total distance/total rate
rate = distance/time

A====================B==========C

If A-B is twice the length of B-C then let A-B = 2d and let B-C = d

Average speed = 3d/(2d/100) + (d/75)
3d/(6d/300) + (4d/300)
3d/(10d/300)
900d/10d
Average speed = 90

ANSWER: D. 90

parthaguna · Answer

Average Speed = total Distance/total Time . 
Average Speed= (2d+d)/{(2d/100)+(d/75)}=3d/(d/30)=90
Answer is D

bumpbot · Answer

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Points A, B, and C lie, in that order, on a straight railroa

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