The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed of 50km/hr between A and B and 60km/hr between B and C, it takes 3 hours to travel from A to C. If it maintains 60km/hr between A and B and 50km/hr between B and C, the journey takes 8 minutes less. What is the distance from A to C via B?
time= distance/speed.
3hrs= d/50 + x/60
2hrs 52min= d/60 + x/50 or
172/60 hrs= d/60 + x/50
I would multiply the first equation by 50, the second by 60
3*50=d-50x/60
172=d-60x/50
subtract the second from the first.
150-172=x(5/6-6/5)
solve for x.
Then, put x in either equation, solve for d. you are looking for x+d
Mathematics
Helo
To find the distance from A to C via B, we need to use the formula:
Distance = Speed * Time
Let's denote the distance from A to B as d km and the distance from B to C as x km.
We are given that a bus maintains an average speed of 50 km/hr between A and B and 60 km/hr between B and C, and it takes 3 hours to travel from A to C.
Using the formula above, we can set up the equation as:
d + x = 50 * 3 + 60 * 3
Simplifying the equation, we get:
d + x = 150 + 180
d + x = 330 ----(1)
Now, we are also given that if the bus maintains 60 km/hr between A and B and 50 km/hr between B and C, the journey takes 8 minutes less. Since 8 minutes is equal to 8/60 = 2/15 hours, the new time from A to C is 3 - 2/15 hours.
Using the formula again, we can set up the second equation as:
d + x = 60 * (3 - 2/15) + 50 * (3 - 2/15)
Simplifying the equation, we get:
d + x = 180 - 4/15 + 150 - 4/15
d + x = 330 - 8/15 ----(2)
Now, we can solve the two equations (1) and (2) to find the values of d and x.
By subtracting equation (2) from equation (1), we get:
0 = 8/15
This means that the two equations are contradictory, and there is no solution.
Hence, there is no valid distance from A to C via B that satisfies the given conditions.