Two towns P and Q are 400 km apart. A bus left for P and Q. It stopped at Q for one hour and then started the return to P. one hour after the departure of the bus from P, a trail also heading for Q left P. the trailer met the returning bus ¾ of the way from P to Q. they met t hours after the departure of the bus from P.
Express the average speed of the trailer in terms of t
Find the ration of the speed of the bus O that of the trailer.
To express the average speed of the trailer in terms of t, we need to calculate the total distance traveled by the trailer and divide it by the time taken. Let's break down the problem step by step.
1. Distance between P and Q: Given as 400 km.
2. Bus journey:
- Initially, the bus left P and traveled towards Q.
- It stopped at Q for one hour.
- After one hour, it started the return journey towards P.
3. Trailer journey:
- The trailer left P one hour after the departure of the bus.
- It was heading towards Q.
- The trailer met the returning bus ¾ (three-fourths) of the way from P to Q.
To solve the problem, let's use some variables:
- Let's assume the speed of the bus as B km/h.
- Let's assume the speed of the trailer as T km/h.
- Let's assume the time taken to meet between the trailer and the bus as t hours.
Now, let's calculate the distances covered by the bus and the trailer:
1. Distance covered by the bus:
- It travels from P to Q (400 km).
- It travels from Q to ¾ of the way back to P (3/4 * 400 = 300 km) in t hours.
2. Distance covered by the trailer:
- It travels from P to ¾ of the way from P to Q (3/4 * 400 = 300 km) in t hours.
Now, let's calculate the average speed of the trailer:
Average speed = Total distance covered / Time taken
The total distance covered by the trailer is 300 km, and the time taken is t hours. So,
Average speed of the trailer = 300 km / t hours
Therefore, the average speed of the trailer in terms of t is 300 km/t.
Now, let's find the ratio of the speed of the bus to that of the trailer:
Ratio of speeds = Speed of the bus / Speed of the trailer
= B km/h / T km/h
Thus, the ratio of the speed of the bus to that of the trailer is B/T.