Boat and Stream

[tass@]

Two boats on the opposite shores of a river start moving towards each other, When they pass each other they are 750 yards from one shoreline. They each continue to the opposite shore, immediately turn around and start back. When they meet again they are 250 yards from the other shoreline. Each boat maintains a constant speed throughout. How wide is the river?

a)2000 b)1800 c) 1000 d) 1200

[GMATinsight]

Then they meet for the first time then distance traveled by the first boat (from the first shore) is 750 in total covered distance covered by both boats together equal to width of River.

If they meet for the second time then they must have traveled the distance (after the first meeting) equal to twice the width of river therefore the distance traveled by the first boat after the first meeting should be 2x750 i.e. 1500. But now the boat is 250 away from the second shore that mean the the boat must have traveled the distance of 1500-250 = 1250 more to reach the other shore.

That means the total distance from one shore to the second shore = 750 (during first meeting) + 1250 (distance to reach the opposite shore = 2000 ANSWER

[GMATinsight]

EXPLANATION AVAILABLE ONLINE:

Let w be the width of the river, and let a and b be the distances covered by the boats by the time they first pass each other.

The sum of these distances is the width of the river, so

(eq. 1) w = a + b

We're told that the boats first pass 750 yards from one shoreline, which means one of the boats traveled 750 yards. Let's say WLOG that

(eq. 2) a = 750

By the second passing, each boat has covered the width of the river, and turned around. Then together, the boats have covered the width of the river once more, so the sum of the distances they've traveled is three times with width of the river. Since they travel at a constant rate, and together they've gone three times as far as when they first passed, it follows that one of them has traveled a distance of 3a and the other has traveled 3b.

When the boats passed a second time, 250 yards from the "other" shoreline, it follows that the same boat that had traveled 750 yards by their first passing has traveled w+250 yards by the second passing.

(eq. 3) 3a = w + 250

Now we have three equations in three unknowns, so it is a snap to solve them.

w = 2000
a = 750
b = 1250

In general, if the boats pass "c" yards from one shore, then both boats hit the opposite bank and turn around, and they pass again "d" yards from the other shore, then the three equations are

(eq. 4) w = a + b
(eq. 5) a = c
(eq. 6) 3a = w + d

which have the solution, in terms of c and d,

w = 3c - d
a = c
b = 2c - d

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Hi tass@,

What is the source of this question? I ask because while the GMAT Quant section WILL include questions that involve the Distance Formula, the Average Speed Formula and even Combined Rate, it won't do so in this fashion.

It's important to use accurate GMAT practice materials during your studies so that you are properly trained for Test Day. This question is not a good use of your time.

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

Two boats on the opposite shores of a river start moving towards each other, When they pass each other they are 750 yards from one shoreline. They each continue to the opposite shore, immediately turn around and start back. When they meet again they are 250 yards from the other shoreline. Each boat maintains a constant speed throughout. How wide is the river?

a)2000 b)1800 c) 1000 d) 1200

Let M and N be the two boats.

First meeting:
M-----><-----N
To meet the first time, M and N work together to travel with width of the river ONCE.

Second meeting:
<-----N M----->
------> <------
To meet the second time, M and N work together to travel the width of the river TWICE.

Thus, for the second meeting, the distances for M and N each DOUBLE.
We can PLUG IN THE ANSWERS, which represent the width of the river.
The first meeting takes place 750 yards from one of the shores.
When the correct answer choice is plugged in, the second meeting will take place 250 yards from one of the shores.

A: Width = 2000
First meeting: M=750, N=1250
M---750---><-------1250-------N

Second meeting: M=1500, N=2500
<---750---N M-------1250------->
--------1750---------><---250---

Success!
The second meeting takes place 250 yards from one of the shores.

The correct answer is A.