A man travels from town a to b at an average speed of 90km/h.on his return journey he takes (one)1 hour less and his speed is 10km/h faster......1.how far apart are towns a and b, .............

..2.what Is his average speed from town a to b and back to a ..

d1 = 90*t.

d2 = 100*(t-1).

1. d1 = d2.
90t = 100(t-1)
90t = 100t-100
90t-100t = -100
-10t = -100
t = 10 h.
d = 90*10 = 900 km

2. V = d/t=(2*900)km/(10+9)h=94.74 km/h.

To solve this problem, we need to use the given information to set up equations and solve for the unknowns.

Let's start by assigning variables to the unknowns:
Let the distance between town A and B be "d" km.
Let the time taken to travel from town A to town B be "t" hours.
Let the average speed from town A to town B be "s" km/h.

Now let's solve the two parts of the problem:

1. Determining the distance between town A and B:
The formula for distance is speed multiplied by time: distance = speed × time. Given that the average speed is 90 km/h and the time is "t" hours, the equation becomes: d = 90t.
On the return journey, the speed is 10 km/h faster, so the speed will be (90 + 10) km/h = 100 km/h. The time taken will be "t - 1" hours. Therefore, the equation for the return journey becomes: d = 100(t - 1).

We can solve these two equations simultaneously to find the value of "t" and consequently the distance "d".
90t = 100(t - 1) [since d = d]
90t = 100t - 100
100t - 90t = 100
10t = 100
t = 10

Now we can determine the distance:
d = 90t = 90 × 10 = 900 km
Therefore, the distance between town A and town B is 900 km.

2. Calculating average speed:
The average speed for the entire round trip is the total distance divided by the total time taken. The total time taken is the time taken from A to B plus the time taken from B back to A.

Time taken from A to B: t = 10 hours (from the previous calculation)
Time taken from B to A: t - 1 = 10 - 1 = 9 hours

Total time taken: 10 + 9 = 19 hours
Total distance: 2d = 2 × 900 = 1800 km

Average speed = Total distance / Total time = 1800 / 19 ≈ 94.74 km/h

Therefore, the average speed from town A to town B and back to town A is approximately 94.74 km/h.