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 1.8m/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 your building is the restaurant?

Answer 1

Answer:

3 blocks

Explanation:

Let t be the time it take for both you and your friend to walk to the restaurant. We can calculate:

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

$s_1 = v_1t = 1.8t$

Similarly the distance (m) from your friend building to the restaurant is your friend speed times his walking time t

$s_2 = v_2t = 1.2t$

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

$s_1 + s_2 = 5b$

$1.8t + 1.2t = 5b$

$3t = 5b$

$t = 5b/3$

$s_1 = 1.8t = 1.8(5b/3) = 3b$

So you are 3b meters from the restaurant, since each block is b meters long, 3b meters would equals to 3b/b = 3 blocks