Hard Level
Dhaka Express and Khulna Express trains left from two stations towards Khulna station and Dhaka station respectively. 3 hours after they met the trains were 675 miles apart. The Dhaka Express arrived at its destination 16 hours after their meeting and the Khulna Express arrived at its destination 25 hours after their meeting. How many hours Dhaka Express ano did it take for the the whole trip?
Piash Khan
Let's solve this problem step by step:
1. Denote:
- \( v_D \) as the speed of the Dhaka Express.
- \( v_K \) as the speed of the Khulna Express.
2. When the trains meet, they have traveled for the same duration, say \( t \) hours.
3. After they meet:
- The Dhaka Express reaches its destination 16 hours later, implying it travels \( v_D \times 16 \) miles.
- The Khulna Express reaches its destination 25 hours later, implying it travels \( v_K \times 25 \) miles.
4. The problem states that 3 hours after meeting, the distance between the two trains is 675 miles, which means:
\[
3v_D + 3v_K = 675 \implies v_D + v_K = 225 \text{ miles per hour}
\]
5. Additionally, since they reach their destinations 16 and 25 hours after the meeting respectively:
\[
v_D \times 16 + v_K \times 25 = d \text{ (where \( d \) is the total distance of the trip)}
\]
### To find the time taken by Dhaka Express for the entire trip:
The time taken by the Dhaka Express for the whole trip would be \( t + 16 \) hours.
Let's find the values of \( v_D \) and \( v_K \), and then calculate \( t + 16 \).
The Dhaka Express took a total of 57 hours for the whole trip.
