# Thread: When Will Two Men Meet?

1. ## When Will Two Men Meet?

Two men start from the same corner "A", going in different directions around a field 1 mile square. The man going along AB walks 4 miles an hour, and the other man who is traveling AD goes 3 miles an hour. Where and after how long will they meet?

2. Hello, magentarita!

Two men start from the same corner $\displaystyle A$,
. . going in different directions around a field 1 mile square.
The man going along AB walks 4 mph, and the other man going along AD goes 3 mph.
Where and after how long will they meet?

One man walks at 4 mph, the other at 3 mph.
They have a combined speed of 7 mph.

How long will it take them to walk a total of 4 miles?
. . It will take them: .$\displaystyle \boxed{\frac{4}{7}}$ of an hour.

The first man walks: .$\displaystyle 4\times \tfrac{4}{7} \:=\:\tfrac{16}{7} \:=\:2\tfrac{2}{7}$ miles.

The second man walks: .$\displaystyle 3 \times \tfrac{4}{7} \:=\:\tfrac{12}{7} \:=\:1 \tfrac{5}{7}$ miles.

They will meet at point $\displaystyle P.$
Code:
           1
A * → → → → * B
↓         ↓
↓         ↓
1 ↓         ↓ 1
↓         ↓
↓         ↓
D * → → * ← * C
P

3. ## wow....

Originally Posted by Soroban
Hello, magentarita!

One man walks at 4 mph, the other at 3 mph.
They have a combined speed of 7 mph.

How long will it take them to walk a total of 4 miles?
. . It will take them: .$\displaystyle \boxed{\frac{4}{7}}$ of an hour.

The first man walks: .$\displaystyle 4\times \tfrac{4}{7} \:=\:\tfrac{16}{7} \:=\:2\tfrac{2}{7}$ miles.

The second man walks: .$\displaystyle 3 \times \tfrac{4}{7} \:=\:\tfrac{12}{7} \:=\:1 \tfrac{5}{7}$ miles.

They will meet at point $\displaystyle P.$
Code:
           1
A * → → → → * B
↓         ↓
↓         ↓
1 ↓         ↓ 1
↓         ↓
↓         ↓
D * → → * ← * C
P
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