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A boat travels from point A to point B upstream and returns from point
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28 Apr 2021, 08:37
28 Apr 2021, 08:37
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A boat travels from point A to point B upstream and returns from point B to point A downstream. If the round trip takes the boat 5 hours and the distance between point A and point B is 120 kms and the speed of the stream is 10 km/hr, how long did the upstream journey take?
A. 2.5 hrs
B. 3 hrs
C. 3.5 hrs
D. 4 hrs
E. 4.5 hrs
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 2.5 hrs
B. 3 hrs
C. 3.5 hrs
D. 4 hrs
E. 4.5 hrs
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Status:Founder & Quant Trainer
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Posts: 1546
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A boat travels from point A to point B upstream and returns from point
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28 Apr 2021, 08:47
28 Apr 2021, 08:47
1
Carcass wrote:
A boat travels from point A to point B upstream and returns from point B to point A downstream. If the round trip takes the boat 5 hours and the distance between point A and point B is 120 kms and the speed of the stream is 10 km/hr, how long did the upstream journey take?
A. 2.5 hrs
B. 3 hrs
C. 3.5 hrs
D. 4 hrs
E. 4.5 hrs
A. 2.5 hrs
B. 3 hrs
C. 3.5 hrs
D. 4 hrs
E. 4.5 hrs
Let the speed of the boat be \(b\)
Speed upstream = \(b - 10\)
Speed downstream = \(b + 10\)
Given: \(t_D + t_U = 5\)
\(\frac{120}{b+10} + \frac{120}{b-10} = 5\)
Solve for \(b = 50\)
\(t_U = \frac{120}{40} = 3\)hrs
Hence, option B
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A boat travels from point A to point B upstream and returns from point
[#permalink]
28 Apr 2021, 08:48
28 Apr 2021, 08:48
1
Carcass wrote:
A boat travels from point A to point B upstream and returns from point B to point A downstream. If the round trip takes the boat 5 hours and the distance between point A and point B is 120 kms and the speed of the stream is 10 km/hr, how long did the upstream journey take?
A. 2.5 hrs
B. 3 hrs
C. 3.5 hrs
D. 4 hrs
E. 4.5 hrs
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 2.5 hrs
B. 3 hrs
C. 3.5 hrs
D. 4 hrs
E. 4.5 hrs
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
GIVEN: Speed of stream = 10 kmh
Let b = the speed of the boat in STILL (current-less) water
So, speed while travelling UPSTREAM = b - 10
And speed while travelling DOWNSTREAM = b + 10
GIVEN: round trip takes the boat 5 hours and the distance between point A and point B is 120 kms
Let's start with a "word equation"
(travel time UPSTREAM) + (travel time DOWNSTREAM) = 5 hours
time = distance/ speed
So we can write: (120/(b - 10)) + (120/(b + 10)) = 5
Multiply both sides by (b - 10) to get: 120 + (120)(b - 10)/(b + 10) = 5(b - 10)
Multiply both sides by (b + 10) to get: 120(b + 10) + (120)(b - 10) = 5(b - 10)(b + 10)
Expands to get: 120b + 1200 + 120b - 1200 = 5b² - 500
Simplify to get: 240b = 5b² - 500
Rearrange to get: 5b² - 240b - 500 = 0
Divide both sides by 5 to get: b² - 48b - 100 = 0
Factor to get (b - 50)(b + 2) = 0
So, EITHER b = 50 OR b = -2
Since the speed cannot be negative, we know that b = 50 kmh
How long did the upstream journey take?
The boat's UPSTREAM speed = b - 10
= 50 - 10
= 40 kmh
time = distance/ speed
So, the boat's travel time upstream = 120/40 = 3 hours
Answer: B
Cheers,
Brent
