A bus travels from Station A to Station B, and a truck travels from Station B to Station A on the same road. The speed of the bus is 54 km/h, and the speed of the truck is 48 km/h. After they pass each other, they continue drive to the destinations. Once they reach the destination, they turn around to continue travel along the same road. When they meet again, the bus travels 216 km more than the truck. What is the distance between the two stations in kilometers?

The distance between the two train stations is 1728 km

Step-by-step explanation:

The speed of the bus = 54 km/h

The speed of the truck = 48 km/h

When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck

Let the distance between the two train stations = x

Let the location where they first meet be y from station A we have;

The location where they meet again = y - 216 km

Therefore, we have;

Location where they

The time for the truck and the bus to meet again = t

Therefore, 54 × t - 48 × t = 216 km

6·t = 216 km

t = 36 hours

Therefore, the time for the bus to travel x + 216 km = 36 hours

54 × 36 = 1944 = x + 216

x = 1944 - 216 = 1728 km

The distance between the two train stations = 1728 km.

1)

Statement Reason
1. ∠1 and ∠3 are vertical angles. 1. Given
2. ∠1 and ∠2 form a linear pair. VAT
∠2 and ∠3 form a linear pair. 2. Definition of linear pair
3. ∠1 and ∠2 are supplementary. Substitution Property
∠2 and ∠3 are supplementary. SAME SIDE INTERIOR ANGLES THEOREM
3. VERTICAL ANGLES THEOREM
4. m∠1 + m∠2 = 180˚ SAME SIDE INTERIOR ANGLES THEOREM
  m∠2 + m∠3 = 180˚ SAME SIDE INTERIOR ANGLES THEOREM
5. m∠1 + m∠2 = m∠2 + m∠3 
(SUBSTITUTION PROPERTY)
6. m∠1 = m∠3 opposite angles
7. ∠1 ≅ ∠3 7. Given