• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

## Relative speed; Boats and Streams; Difficulty: Hard

tagged by: Alphonsaj

This topic has 2 expert replies and 1 member reply
Alphonsaj Newbie | Next Rank: 10 Posts
Joined
14 Jul 2016
Posted:
8 messages

#### Relative speed; Boats and Streams; Difficulty: Hard

Sat Jul 16, 2016 11:58 pm
A ship of length 300 metres is moving upstream on Suez canal and crosses a boat floating freely on the same stream in 30 seconds. If the speed of the stream is 10mph what is the still water speed of the ship?

A. 26kmph
B. 20kmph
C. 24kmph
D. 46kmph
E. 36kmph

Source: 4gmat

E

### Top Member

regor60 Master | Next Rank: 500 Posts
Joined
15 Oct 2009
Posted:
261 messages
27
Mon Jul 18, 2016 6:36 am
Recognize that the ship's speed relative to the water reflects adding the speed of the water against ground and the speed of the ship against ground since both are working against the same distance, 300 meters.

Recognize that the the free floating boat is just a point on the water reflecting the water speed

Let Rate of Ship against ground = Rs
" Boat = Rb = water speed against ground
" Rsb = Rate of Ship relative to Boat > Still water speed> as if water not moving

Distance covered = 300 meters = Rsb x Time

Time = 30 seconds = 1/120 hr

Solve for Rsb = 300m/(1/120)hr = 36000meters/hr = 36kmh

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
625
Target GMAT Score:
V51
GMAT Score:
780
Wed Jul 20, 2016 11:01 pm
The wording here is quite poor ("crosses a boat" is unintelligible), but I think the idea is something like

Quote:
A ship of length 300 meters is traveling upstream at a constant rate on the Suez Canal, which has its own constant rate of 10 km/h. The ship encounters a boat, which is floating freely down the Canal. (Assume the boat has zero weight, and is traveling only under the power of the stream.) If the time from when the ship meets the boat to when the ship passes the boat is 30 seconds, what is the speed of the ship in still water
Let's call the ship's rate in still water s. We know that

(Ship's Rate + Boat's Rate) * 30 seconds = 300 meters

since the ship and the boat are working together to traverse the full 300 meters. (The ship is doing one part of the distance, and the boat is doing the rest, so we can add their rates together.)

We also know that the ship's rate against the current = (s - 10), and the boat's rate with the current is 10, so we have

(s - 10 + 10) * 30 seconds = 300 meters

s = 300 meters/30 seconds = 10 meters/second

To convert this to kilometers per hour, we multiply the top by 60*60 and the bottom by 100, which gives us 36 kilometers/hour.

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
625
Target GMAT Score:
V51
GMAT Score:
780
Wed Jul 20, 2016 11:05 pm
That said, I'm not sure my interpretation is correct ... but it does get me to the OA, and seems like the intent of the question!

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### Top First Responders*

1 GMATGuruNY 87 first replies
2 Brent@GMATPrepNow 66 first replies
3 Rich.C@EMPOWERgma... 35 first replies
4 Jay@ManhattanReview 25 first replies
5 Sionainn@Princeto... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

142 posts
2 GMATGuruNY

The Princeton Review Teacher

128 posts
3 Jeff@TargetTestPrep

Target Test Prep

123 posts
4 Scott@TargetTestPrep

Target Test Prep

102 posts
5 Max@Math Revolution

Math Revolution

88 posts
See More Top Beat The GMAT Experts