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Tricky speed-distance-time question: Bill travels from...

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by Brent@GMATPrepNow » Mon Apr 17, 2017 5:28 am
Bill travels from point A to point B at a constant speed of 120 kilometers per hour. Upon reaching point B, he immediately heads back to point A. On his return trip to point A, Bill spends half the time traveling 20 kilometers per hour, and half the time traveling 60 kilometers per hour. What is Bill's average speed, in kilometers per hour, for the entire roundtrip?

A) 48
B) 60
C) 66 2/3
D) 72
E) 80

Answer: B

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by regor60 » Mon Apr 17, 2017 10:28 am
Let D = distance from A to B

Given that Distance = Rate x Time, let T1 = D1/20 equal time spent travelling 20 kph.

Similarly, let T2 = (D-D1)/60 equal time spent travelling 60 kph

Since these times are equal, D1/20 = (D-D1)/60. Solving for D1 = D/4. Therefore, distance travelled at 60 kph = D-D/4 or 3D/4

Time spent on trip from A to B = D/120. Time spent travelling 20 kph = (D/4)/20 = D/80. Note that time spent travelling 60 kph is given to be the same, also D/80.

Average speed = total distance travelled/total time = 2D/[(D/120 + (D/80)+(D/80)]

Notice the D's cancel in numerator and denominator. Common denominator is 240, so:

2/[(2/240)+(3/240)+(3/240)] = 2/(8/240) = 240/4 = 60
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by DavidG@VeritasPrep » Mon Apr 17, 2017 12:31 pm
Brent@GMATPrepNow wrote:Bill travels from point A to point B at a constant speed of 120 kilometers per hour. Upon reaching point B, he immediately heads back to point A. On his return trip to point A, Bill spends half the time traveling 20 kilometers per hour, and half the time traveling 60 kilometers per hour. What is Bill's average speed, in kilometers per hour, for the entire roundtrip?

A) 48
B) 60
C) 66 2/3
D) 72
E) 80

Answer: B

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Brent original!

Because on the return trip we spend an equal amount of time traveling at 20mph and 60mph, the average speed for the return trip is 40mph. Now pick a simple number for the distance. Say we go 120 miles.The trip there will take 1 hour at 120mph. The trip back will take 3 hours at 40mph.

Total time = 1 + 3 = 4 hours.

Total distance = 120 + 120 = 240 miles

Average speed for trip = 240/4 = 60mph, or B
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by GMATGuruNY » Tue Apr 18, 2017 7:08 am
Brent@GMATPrepNow wrote:Bill travels from point A to point B at a constant speed of 120 kilometers per hour. Upon reaching point B, he immediately heads back to point A. On his return trip to point A, Bill spends half the time traveling 20 kilometers per hour, and half the time traveling 60 kilometers per hour. What is Bill's average speed, in kilometers per hour, for the entire roundtrip?

A) 48
B) 60
C) 66 2/3
D) 72
E) 80
Alternate approach:

On the return trip from B to A, let Bill spend 1 hour traveling at 20mph and 1 hour traveling at 60mph, for a total of 2 hours and 80 miles.
At a rate of 120mph, the time to travel the 80 miles from A to B = d/r = 80/120 = 2/3 hour.
Average speed for the whole trip = (total distance)/(total time) = (80+80)/(2 + 2/3) = 160/(8/3) = 60mph.

The correct answer is B.
Last edited by GMATGuruNY on Tue Apr 18, 2017 7:12 am, edited 1 time in total.
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by Brent@GMATPrepNow » Tue Apr 18, 2017 7:12 am
Brent@GMATPrepNow wrote:Bill travels from point A to point B at a constant speed of 120 kilometers per hour. Upon reaching point B, he immediately heads back to point A. On his return trip to point A, Bill spends half the time traveling 20 kilometers per hour, and half the time traveling 60 kilometers per hour. What is Bill's average speed, in kilometers per hour, for the entire roundtrip?

A) 48
B) 60
C) 66 2/3
D) 72
E) 80
Let's assign a nice value to the distance between point A and point B.
Given the 3 speeds (120 kmh, 20 kmh and 60 kmh), it seems that a distance of 120 kilometers will work nicely.

Bill travels from point A to point B at a constant speed of 120 kilometers per hour.
Time = distance/rate
= 120/120 = 1 hour

On his return trip to point A, Bill spends half the time traveling 20 kilometers per hour, and half the time traveling 60 kilometers per hour.
Let x = the distance traveled at 20 kilometers per hour
So, 120 - x = the distance traveled at 60 kilometers per hour

Word equation: TIME traveled at 20 kmh = TIME traveled at 60 kmh
Time = distance/rate
So, we get: x/20 = (120-x)/60
Cross multiply: 60x = 20(120-x)
Expand: 60x = 2400 - 20x
Solve: x = 30
So, Bill drove 30 kilometers at 20 kilometers per hour, which means he drove the other 90 kilometers at 60 kilometers per hour.

TIME traveled at 20 kmh = 30/20 = 1.5 hours
Since the two travel times are EQUAL, we also know that Bill drove 1.5 hours at 60 kilometers per hour

So, the TOTAL DISTANCE = 120 + 120 = 240 kilometers
So, the TOTAL TRAVEL TIME = 1 + 1.5 + 1.5 = 4 hours

Average speed = (TOTAL DISTANCE)/(TOTAL TRAVEL TIME) = 240/4 = 60 kilometers per hour

Answer: B
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