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A cruise ship traveled for 3 hours. In the first hour, the ship sailed

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A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 23 Jul 2018, 19:46
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A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour. In the middle hour the ship sailed at the average speed of the first and third hours. What was the total distance of the ship during the 3 hours of sailing?

A. 65.
B. 66.5.
C. 67.5.
D. 70.
E. 72.5

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A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 23 Jul 2018, 19:54
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A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour.

Let x be the speed of the cruise ship in the third hour

=> speed of the cruise ship in first hour \(\frac{125}{100} * x\) = 25

=> x = \(25 * \frac{4}{5}\)

=> x = 20

Speed of the cruise ship in second hour = \(\frac{20 + 25}{2} = 22.5\)

=> Total distance traveled by cruise ship = 25 + 22.5 + 20 = 67.5

Hence option C
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Re: A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 24 Jul 2018, 01:54
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Bunuel wrote:
A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour. In the middle hour the ship sailed at the average speed of the first and third hours. What was the total distance of the ship during the 3 hours of sailing?

A. 65.
B. 66.5.
C. 67.5.
D. 70.
E. 72.5



The ship traveled at the speed of 25 Km/h in the first hour
1.25x=25 --> x = 20
in the second hour 20 Km/h
and in the third hour (25+20)/2=22.5 Km/h
total distance = 25+20+22.5=67.5 Km
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Re: A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 24 Jul 2018, 07:33
Bunuel wrote:
A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour. In the middle hour the ship sailed at the average speed of the first and third hours. What was the total distance of the ship during the 3 hours of sailing?

A. 65.
B. 66.5.
C. 67.5.
D. 70.
E. 72.5


Speed in 1st Hour is 25 Km/Hr
Speed in 3rd Hour is 25/125*100 = 20 Km//Hr
Speed in 2nd Hour is (20 + 25)/2 = 22.50 Km/Hr

Thus the total distance traveled by ship is 25 Kk + 20Km + 22.50 Km = 67.50 Km, Answer must be (C)
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A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 24 Jul 2018, 08:48
Bunuel wrote:
A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour. In the middle hour the ship sailed at the average speed of the first and third hours. What was the total distance of the ship during the 3 hours of sailing?

A. 65.
B. 66.5.
C. 67.5.
D. 70.
E. 72.5

This question has a lot of words, but its premise is very simple. The speed of each segment is the distance of each segment.

Each segment is 1 hour. Speeds are in km per HOUR. Hours cancel. Speed = distance.
\((r*t)=D\)
\((X\frac{km}{hour}*1 hr)=X\) km = \(D\)

Leg 1 speed: 25 kmh

Leg 3 speed. Leg 1 speed is 25% faster than Leg 3 speed. 25% faster =\(1.25=1\frac{1}{4}=\frac{5}{4}\)
Leg 3 speed: \((25=\frac{5}{4}L_3)\) => \((\frac{4}{5}*25=L_3)\)
Leg 3 speed: 20 kmh

Leg 2 speed: ave. of 25 and 20 = 22.5 kmh

Each distance equals each leg's speed.

Leg 1, distance: \(25\frac{km}{hour}*1hr=\) 25 km
Leg 2, distance: 22.5 km
Leg 3, distance: 20 km

Total distance: \((25+22.5+20)=67.5\) km

Answer C
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Re: A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 24 Jul 2018, 09:39
Bunuel wrote:
A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour. In the middle hour the ship sailed at the average speed of the first and third hours. What was the total distance of the ship during the 3 hours of sailing?

A. 65.
B. 66.5.
C. 67.5.
D. 70.
E. 72.5


OA: C
Let the speed of speed in 3rd hour be x
Speed of ship in 1st hour : 25Km/h=1.25x; x=20Km/h
Speed of ship in 2nd hour: (20+25)/2 =22.5 Km/h
Distance travelled by Ship in 3 hour = 25*1+22.5*1+20*1 = 67.5 Km
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Re: A cruise ship traveled for 3 hours. In the first hour, the ship sailed  [#permalink]

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New post 25 Jul 2018, 16:44
Bunuel wrote:
A cruise ship traveled for 3 hours. In the first hour, the ship sailed at a speed of 25 Km/h, which was 25% faster than the speed in the third hour. In the middle hour the ship sailed at the average speed of the first and third hours. What was the total distance of the ship during the 3 hours of sailing?

A. 65.
B. 66.5.
C. 67.5.
D. 70.
E. 72.5


The speed in the first hour is 25 km/h, and the distance traveled is 25 km.

The speed in the third hour is 25/1.25 = 2500/125 = 20 km/h, and the distance traveled is 20 km.

The speed in the second hour is (20 + 25)/2 = 45/2 = 22.5 km/h, and the distance traveled is 22.5 km.

Thus, the total distance traveled is 25 + 20 + 22.5 = 67.5.

Answer: C
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Re: A cruise ship traveled for 3 hours. In the first hour, the ship sailed &nbs [#permalink] 25 Jul 2018, 16:44
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