Two people, one on a motorcycle and one on a bicycle, start from two cities that are 450 km apart and head towards each other. They meet after 2 hours and 30 minutes. If the person on the motorcycle is twice as fast as the person on the bicycle, find the speed of the person on the motorcycle.

1. Problem Description

Two people, one on a motorcycle and one on a bicycle, start from two cities that are 450 km apart and head towards each other. They meet after 2 hours and 30 minutes. If the person on the motorcycle is twice as fast as the person on the bicycle, find the speed of the person on the motorcycle.

2. Solution Steps

Let $v_m$ be the speed of the motorcyclist and $v_b$ be the speed of the cyclist.

We are given that the distance between the two cities is 450 km.

They meet after 2 hours and 30 minutes, which is 2.5 hours.

We are given that $v_m = 2v_b$.

When they meet, the sum of the distances they have traveled is equal to the total distance between the cities.

Distance traveled by the motorcyclist is $d_m = v_m \times t$, where $t = 2.5$ hours.

Distance traveled by the cyclist is $d_b = v_b \times t$, where $t = 2.5$ hours.

Therefore, $d_m + d_b = 450$.

Substituting $d_m = v_m \times 2.5$ and $d_b = v_b \times 2.5$, we get:

$2.5 v_m + 2.5 v_b = 450$

Divide by 2.5:

$v_m + v_b = \frac{450}{2.5} = 180$

We know that $v_m = 2v_b$, so $v_b = \frac{v_m}{2}$.

Substituting this into the equation $v_m + v_b = 180$, we get:

$v_m + \frac{v_m}{2} = 180$

$\frac{3}{2} v_m = 180$

$v_m = \frac{2}{3} \times 180 = 2 \times 60 = 120$

The speed of the motorcyclist is 120 km/h.

3. Final Answer

B. 120 km/ц