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# A motorboat, traveling 30 miles per hour faster than a certain cargo

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Math Expert
Joined: 02 Sep 2009
Posts: 56300
A motorboat, traveling 30 miles per hour faster than a certain cargo  [#permalink]

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07 May 2017, 12:08
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:02) correct 38% (02:17) wrong based on 130 sessions

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A motorboat, traveling 30 miles per hour faster than a certain cargo ship, leaves the dock 2 hours after that cargo ship leaves the same dock. If the two boats take the same route and the motorboat catches the cargo ship in 3 hours after the motorboat leaves the dock, then what is the motorboat's rate?

A. 75
B. 45
C. 30
D. 15
E. 10

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Re: A motorboat, traveling 30 miles per hour faster than a certain cargo  [#permalink]

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07 May 2017, 12:21
1
Bunuel wrote:
A motorboat, traveling 30 miles per hour faster than a certain cargo ship, leaves the dock 2 hours after that cargo ship leaves the same dock. If the two boats take the same route and the motorboat catches the cargo ship in 3 hours after the motorboat leaves the dock, then what is the motorboat's rate?

A. 75
B. 45
C. 30
D. 15
E. 10

A: 75

Let speed of motorboat be = M
Let speed of cargo be =C
M=30+C

Total Time for M=3
Total time for C=5

Distance travelled by M and C is equal;

Therefore,
5C=3M
=> 5C=3C+90
=>C=45

Therefore, M=45+30=75
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Re: A motorboat, traveling 30 miles per hour faster than a certain cargo  [#permalink]

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07 May 2017, 12:34
1
Let the speed of the cargo boat be x. Hence the motor boat has speed x+30. Time at which the cargo ship leaves is t, since the motor boat leaves 2 hours later, time of motor boat is t+2

Since the motorboat catches with the cargo ship in 3 hours, distance travelled by both the cargo ship and motor boat is the same.

(x+30)3 = 5x
3x + 90 = 5x
2x = 90 or x=45

Hence speed of motor boat is 75(Option A)
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Re: A motorboat, traveling 30 miles per hour faster than a certain cargo  [#permalink]

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31 Dec 2017, 13:51
Let the speed of the slower boat be x. So in two hours it has gone a distance of 2x. Every hour the faster boat goes 30 more miles than the slower boat. In three hours it has gone 90 more miles, but the slower boat started off ahead by 2x. Since they are at the same position after the faster boat has gone for 3 hours we can say. 90-2x=0. x=45. So the faster one goes 75 mph
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Re: A motorboat, traveling 30 miles per hour faster than a certain cargo  [#permalink]

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31 Dec 2017, 15:30
Bunuel wrote:
A motorboat, traveling 30 miles per hour faster than a certain cargo ship, leaves the dock 2 hours after that cargo ship leaves the same dock. If the two boats take the same route and the motorboat catches the cargo ship in 3 hours after the motorboat leaves the dock, then what is the motorboat's rate?

A. 75
B. 45
C. 30
D. 15
E. 10

ratio of MB rate to CS rate=r/(r-30) mph
ratio of MB time to CS time=3/5 hr
inverting, r/(r-30)=5/3
r=75 mph
A
Re: A motorboat, traveling 30 miles per hour faster than a certain cargo   [#permalink] 31 Dec 2017, 15:30
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