Question

You and a friend work in buildings five equal-length blocks apart, and you plan to meet for lunch. Your friend strolls leisurely at 1.2 m/s, while you like a brisker pace of 1.6 m/s. Knowing this, you pick a restaurant between the two buildings at which you and your friend will arrive at the same instant if both of you leave your respective buildings at the same instant. In blocks, how far from the wife’s building is the restaurant?

Answer 1

Your friend is 2.143 blocks from the restaurant.

You are 2.857 blocks from the restaurant.

Step-by-step explanation:

Let t be the time both you and your friend take to walk to the restaurant.

The distance (m) from your building to the restaurant is your walking time t times your speed v1

`s_1 = v_1t = 1.6t`

Similarly the distance (m) from your friend building to the restaurant:

`s_2 = v_2t = 1.2t`

Let b be the length (in m) of a block, the total distance of 5 blocks is 5b

`s_1 + s_2 = 5b`

`1.6t + 1.2t = 5b`

`2.8t = 5b`

`t = 5b/2.8 = 25b/14`

`s_2 = 1.2t = 1.2(25b/14) = 2.143b`

So your friend are 2.143b meters from the restaurant, since each block is b meters long, 2.143b meters would equals to 2.143b/b = 2.143 blocks. And you are 5 - 2.143 = 2.857 blocks from the restaurant.