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.

Question

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

(b) Find the ratio of the speed of the bus so that of the trailer.

Answer 1

see related questions below

Answer 2

(a) 3/4*400 = 300 Km

Speed = 300/t km/hr
(b) Speed Of Bus (400+100)/t=500/t
(500/t)/(300/t)
The Ratio Is 5:3

Answer 3

To solve this problem, we need to analyze the distances and times involved.

Let's denote the speed of the bus as B (in km/h) and the speed of the trailer as T (in km/h).

(a) Express the average speed of the trailer in terms of t:

Since the bus stops at Q for one hour before starting its return journey, it is on the road for a total of t+1 hours. During this time, it travels a distance of 400 km.

So the average speed of the bus, assuming constant speed, is given by:
Average speed = Total distance / Total time
B = 400 / (t + 1) (equation 1)

Now, let's consider the trailer. It starts 1 hour after the departure of the bus from P and meets the returning bus 3/4 of the way from P to Q.

The distance traveled by the trailer when it meets the bus is (3/4) * 400 = 300 km.

The time taken for the trailer to reach this point can be calculated using its speed, T, as:
Time = Distance / Speed
Time = 300 / T

The total time for the trailer to meet the bus is the time it takes to reach the meeting point plus the 1-hour delay in departure:
Total time = (300 / T) + 1

Therefore, the average speed of the trailer is given by:
Average speed = Total distance / Total time
T = 400 / ((300 / T) + 1) (equation 2)

Simplifying equation 2, we get:
T = (400T) / (300 + T) (cross-multiplication)

Now we can solve this equation to express the average speed of the trailer in terms of t.

(b) Find the ratio of the speed of the bus to that of the trailer:

To find the ratio of the speed of the bus to that of the trailer, we can divide equation 1 by equation 2:

(B / T) = (400 / (t + 1)) / [(400T) / (300 + T)]

Simplifying this expression gives:
(B / T) = (300 + T) / (t + 1)

Therefore, the ratio of the speed of the bus to that of the trailer is (300 + T) / (t + 1).