Two buses start from opposite points on a straight main road that is apart. The first bus runs for , takes a right turn, and runs for . It then turns left, runs for another , and then takes a turn to head back to reach the main road. In the meantime, due to a minor breakdown, the second bus has run only along the main road. What is the distance between the two buses at this point?
- A65 km
- B75 km
- C80 km
- D85 km
Solution & Step-by-step Explanation
Let the straight main road be represented along a horizontal axis from point () to point ().
* Total length of main road .
**First Bus Path (starting from towards ):**
1. Travels along the main road. Horizontal position .
2. Turns right and travels away from the main road.
3. Turns left and travels parallel to the main road.
4. Turns back towards the main road to reach it.
Upon returning to the main road, its horizontal distance covered along the main road is:
**Second Bus Path (starting from towards ):**
1. It travels straight along the main road for .
Its position measured from point is:
Distance between the two buses:
Since both buses are now back on the straight main road, the direct distance between them is:
* Total length of main road .
**First Bus Path (starting from towards ):**
1. Travels along the main road. Horizontal position .
2. Turns right and travels away from the main road.
3. Turns left and travels parallel to the main road.
4. Turns back towards the main road to reach it.
Upon returning to the main road, its horizontal distance covered along the main road is:
**Second Bus Path (starting from towards ):**
1. It travels straight along the main road for .
Its position measured from point is:
Distance between the two buses:
Since both buses are now back on the straight main road, the direct distance between them is: