Question

A person travels from city A to city B. If he travels at a speed of 50 km/h, he arrives 1 hour early. if he travels at a speed of 30 km/h, he arrives 1 hour late What is the distance (in km) between city A and city B ?

• A. 150 km
• B. 120 km
• C. 200 km
• D. 180 km

Answer 1

Answer:

A. 150 km

Let the distance between A and B be (D) km, and the scheduled travel time be (T) hours.

Case 1: Speed = 50 km/h (1 hour early)

$\frac{D}{50} = T - 1$

Speed = 30 km/h (1 hour late)

$\frac{D}{30} = T + 1$

Subtract equations

$\frac{D}{30} - \frac{D}{50} = (T+1) - (T-1)$

$\frac{D}{30} - \frac{D}{50} = 2$

Find LCM of 30 and 50 = 150:

$\frac{5D - 3D}{150} = 2$

$\frac{2D}{150} = 2$

$\frac{D}{75} = 2$

$D = 150$

Final Answer

$\boxed{150 \text{ km}}$