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.
(a) Express the average speed of the trailer in terms of t
(t +1) ¾ = 400 + t
(b) Find the ration of the speed of the bus so that of the trailer.
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.