A man drives from ibadan to Oyo, a distance of 48km in 45 minutes. If he drives at 72km/h where the surface is good and 48km/h where it is bad, find the number of kilometres of good surface.
total time = 45 min .75 hour
72 t + 48(.75-t) = 48 etc
thank you, but where do you get 75 hr?
Look carefully, Damon had .75 not 75
45 minutes
= 3/4 hour
= .75 hours
To find the number of kilometers of good surface, we need to first determine the time it took to drive on the good surface and the time it took to drive on the bad surface.
Let's let:
- x be the number of kilometers driven on the good surface
- y be the number of kilometers driven on the bad surface
Given that the total distance traveled is 48 km and the total time taken is 45 minutes, we can set up two equations based on the given speeds:
Equation 1: x kilometers at 72 km/h
Equation 2: y kilometers at 48 km/h
Using the formula time = distance / speed, we can express the time taken for each equation:
Equation 1: x km / 72 km/h = (x/72) hours
Equation 2: y km / 48 km/h = (y/48) hours
Since the total time taken is 45 minutes, we can convert it to hours by dividing by 60:
Total time taken = 45 minutes / 60 = 0.75 hours
Now, we can set up an equation based on the total time taken:
Equation 3: (x/72) + (y/48) = 0.75
Rearranging Equation 3, we get:
(x/72) + (y/48) - 0.75 = 0
To solve for x, we can rewrite Equation 3 as:
(x/72) = 0.75 - (y/48)
Simplifying further:
x = 0.75 * 72 - (y/48) * 72
x = 54 - (3/2)y
Since x + y = 48 km, we can substitute x in terms of y in the above equation:
54 - (3/2)y + y = 48
Simplifying:
(3/2 - 1)y = 54 - 48
(1/2)y = 6
y = 12
Now, substituting the value of y in the equation x + y = 48:
x + 12 = 48
x = 48 - 12
x = 36
Therefore, the man drove 36 km on the good surface.