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Explain Bot To solve this problem, we can use the concept of relative speed. Let's break down the information given:
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 trailer 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.
(a) Express the average speed of the trailer in terms of t:
To determine the average speed of the trailer, we need to find the distance traveled by the trailer and divide it by the time taken.
Let's consider the distance from P to the point where the trailer and the bus meet. The distance from P to Q is 400 km. The trailer meets the bus ¾ of the way from P to Q, which means it has traveled (3/4) * 400 km = 300 km when they meet.
The time taken for the trailer to meet the bus is t hours.
Therefore, the average speed of the trailer is:
Speed = Distance / Time
Speed = 300 km / t hours
Speed = 300/t km/h
So, the average speed of the trailer in terms of t is 300/t km/h.
(b) Find the ratio of the speed of the bus to that of the trailer:
The ratio of the speed of the bus to that of the trailer can be found by considering the distance traveled by each.
The bus travels a total distance of 400 km from P to Q and then back to P.
The trailer travels a distance of 300 km from P to the point where they meet.
The time taken by the bus to complete the round trip is t + 1 hour (including the one-hour stop at Q).
The time taken by the trailer to cover 300 km is t hours.
Now, using the formula Speed = Distance / Time, we can determine the ratio of their speeds:
Ratio = Bus Speed / Trailer Speed
Ratio = (400 km + 400 km) / (300 km / t hours)
Ratio = 800 km / (300 km / t hours)
Ratio = (800 km * t hours) / 300 km
Ratio = (8/3) * t
Therefore, the ratio of the speed of the bus to that of the trailer is (8/3) * t.