Two towns P and Q are 400 km apar. 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 buse from P, a trail also heading for Q left P. the trailer meth the returning bus ¾ of the way from P to Q. they met t hours after the departure of the buse from from P.
(a) Epress the average speed of the trailer in terms of t
(b) Find the ration of the speed of the bus O that of the trailer
To solve this problem, let's break it down step by step:
Step 1: Calculate the distance between towns P and Q.
Given that towns P and Q are 400 km apart, the total distance from P to Q (or from Q to P) is 400 km.
Step 2: Calculate the total time taken by the bus.
The bus travels from P to Q and then returns from Q to P. In total, the bus travels twice the distance between P and Q. Let's assume the average speed of the bus is Vb and the time it takes for the bus to travel from P to Q is T. Thus, we can express the total time taken by the bus as 2T.
Step 3: Calculate the time spent by the bus at town Q.
The bus stops at town Q for one hour.
Step 4: Calculate the time taken by the trailer to meet the returning bus.
The trailer starts from P one hour after the bus leaves. So, the time taken by the trailer to meet the returning bus is T - 1 (as the bus has traveled for 1 hour before the trailer starts).
Step 5: Express the average speed of the trailer in terms of T.
The average speed of an object can be calculated by dividing the total distance traveled by the total time taken. In this case, the trailer travels 3/4 of the distance between P and Q before meeting the returning bus. So, the distance traveled by the trailer is (3/4) * 400 km = 300 km. The time taken by the trailer is T - 1. Therefore, the average speed of the trailer is 300 km / (T - 1) hours.
(a) Express the average speed of the trailer in terms of T:
The average speed of the trailer in terms of T is 300 km / (T - 1) hours.
(b) Find the ratio of the speed of the bus to that of the trailer:
The speed of the bus is Vb, and the speed of the trailer is 300 km / (T - 1) hours. The ratio of the speed of the bus to that of the trailer is Vb / (300 km / (T - 1) hours).