a man travelled xhrs at 5km/hr and yhrs at 8km/hr .Distance travelled altogether is 20km. find x and y if the average speed for the journey is 7km/hr
avg speed=20km/time
time=20/7 hrs
but
20=x*5+7(20/7-x)8
solve for x, then y=20/7 -x
To find the values of x and y, we need to set up an equation using the given information.
Let's assume that x and y represent the number of hours the man traveled at 5 km/hr and 8 km/hr, respectively.
The total distance traveled can be calculated by adding the distances traveled at each speed:
Distance traveled at 5 km/hr = (5 km/hr) * x hrs = 5x km
Distance traveled at 8 km/hr = (8 km/hr) * y hrs = 8y km
Since the total distance traveled is given as 20 km, we can set up the equation:
5x + 8y = 20
To find the average speed, we can use the formula:
Average Speed = Total Distance / Total Time
The total time can be calculated by adding x and y:
Total Time = x + y
Since the average speed is given as 7 km/hr, we can set up another equation:
7 = 20 / (x + y)
We now have a system of equations:
5x + 8y = 20
7 = 20 / (x + y)
To solve this system, we can use substitution or elimination method.
Let's rearrange the second equation to find a value in terms of x or y:
7(x + y) = 20
Dividing both sides by 7, we get:
x + y = 20 / 7
We can now substitute this value into the first equation:
5x + 8(20/7 - x) = 20
Now, we can solve the equation for x:
5x + 160/7 - 8x = 20
-3x = 20 - 160/7
-3x = (140 - 160) / 7
-3x = -20/7
x = (-20/7) / -3
x = 20/7 * 1/3
x = 20/21
To find the value of y, we can substitute the value of x into the equation:
y = 20 / 7 - x
y = 20 / 7 - 20/21
y = (20 * 3 - 20) / (7 * 3)
y = 40/21
Therefore, the values of x and y are x = 20/21 and y = 40/21, respectively.