Aptitude Discussion

Q. |
Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide? |

✖ A. |
\(\dfrac{1}{12}\) |

✖ B. |
\(\dfrac{1}{6}\) |

✔ C. |
\(\dfrac{1}{4}\) |

✖ D. |
\(\dfrac{1}{3}\) |

**Solution:**

Option(**C**) is correct

The boats will be colliding after a time which is given by:

\(=\dfrac{20}{5+10}\)

\(=\dfrac{4}{3}\) hr

\(=80\) min

After this time of 80 minutes, boat (1) has covered:

\(=80\times \dfrac{5}{60}\)

\(=\dfrac{20}{3}\)km

whereas boat (2) has covered:

\(=80\times \dfrac{10}{60}\)

\(=\dfrac{40}{3}\) km

After 79 minutes, distance covered by the first boat ($D_1$):

\(=\left(\dfrac{20}{3}-\dfrac{5}{60}\right)\)

After 79 minutes, distance covered by the second boat ($D_2$):

\(=\left(\dfrac{40}{3}-\dfrac{10}{60}\right)\)

So the separation between the two boats:

\(= 20-(D_1-D_2)\)

\(=\dfrac{1}{4}\)km

**Alternative Method:**

Relative speed of two boats:

$=5+10=15$ km/hr

i.e. in 60 min they cover (together) = 15 km

In 1 min they will cover (together) = \(=\dfrac{15}{60}=\dfrac{1}{4}\) km

**Abhijeet**

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my idea is not to bring them together towards the meeting point..but to send them away from the meeting point in 1 minute of time..hope u get it!

**Rohit Sharma**

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alternate solution:

relative speed of boats: 5 kmph +10 kmph = 15 kmph

we have to find the distance between two boats 1 min before colliding:

distance before colliding = distance they have to cover to collide

=> distance 1 min before colliding = distance to be covered in 1 min

so basically we have to find the distance to be covered in 1 min, i.e,

in 1 hr => 15km

in 60min => 15km

in 1 min => (15/60)km

=> (1/4)km

best alternate solution..

start from the point they meet as origin on a number line and add the distance they cover in 1 minute

i.e.,

boat 1 covers 5 * 1/60 = 5/60

boat 2 covers 10 *1/60= 10/60

adding both we get 1/4 of a km