A train traveled for 6 hours. It moved at a constant rate of 40 miles

Question

A train traveled for 6 hours. It moved at a constant rate of 40 miles per hour for the first 3 hours, then increased its speed to a constant rate of 60 miles per hour for the next 3 hours. What was the train's approximate average speed, in miles per hour, over the first half of the distance traveled?

(A) 40
(B) 43
(C) 47
(D) 50
(E) 54

Show Answer

Official Answer

B

(A) 40
(B) 43
(C) 47
(D) 50
(E) 54

sanjitscorps18 · Answer

Total distance is 40 x 3 = 120 miles and 60 x 3 = 180 miles
Total distance = 300 miles.

First half of the distance traveled = 150 miles

Average speed = 150 / (3 + 1/2) = 300 / 7 = 42.8 ≈ 43

IMHO Option B

Vishal3455 · Answer

Formula for 
Average speed= Total Distance/Total Time

Here Train travelled total of 300km (40×2+60×3)

Now for average speed of half distance i.e. 150km

Time taken=3 hrs as for 120km and for next 30km at speed of 60 it would take 
 0.5  hrs

average speed= 150/3.5(3+0.5)

Which is approx= 43

Posted from my mobile device

Kinshook · Answer

Given: A train traveled for 6 hours. It moved at a constant rate of 40 miles per hour for the first 3 hours, then increased its speed to a constant rate of 60 miles per hour for the next 3 hours.

Asked: What was the train's approximate average speed, in miles per hour, over the first half of the distance traveled?

Total distance travelled = 40*3 + 60*3 = 120 + 180 = 300 miles
Total time = 6 hours

First Half of distance travelled = 150 miles
Time taken = 3 + 30/60 = 3.5 hours
Average speed = 150/3.5 = 300/7 = 42 6/7 = 43 mph

IMO B

Sghodesh · Answer

Why is it not (1/2*Total Distance)/ Total time = 0.5*300/6= 25 ?

Bunuel · Answer

Total Distance/Total time gives the average speed for the entire trip. Then, when you multiply it by 1/2, you just get half of the average speed, so it does not make sense. To get the average speed for the first 150 kilometers, you should divide that by the time spent to cover that distance.

unraveled · Answer

A train traveled for 6 hours. It moved at a constant rate of 40 miles per hour for the first 3 hours, then increased its speed to a constant rate of 60 miles per hour for the next 3 hours. What was the train's approximate average speed, in miles per hour, over the first half of the distance traveled?

(A) 40
(B) 43
(C) 47
(D) 50
(E) 54

Show Answer

Official Answer

B

(A) 40
(B) 43
(C) 47
(D) 50
(E) 54

Total distance = 40*3+60*3 = 300 miles
In first 3 hour train travels 40*3 = 120 miles

Next 30 miles is travelled in 1/2 hour as speed is 60 miles/hour.
Total time taken for first half of the distance(150 miles) covered = 3 + 1/2 hours
 Average speed = 150/3.5 = ~43miles/hour

Answer B.

bumpbot · Answer

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A train traveled for 6 hours. It moved at a constant rate of 40 miles

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A train traveled for 6 hours. It moved at a constant rate of 40 miles

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