Answer:
Mbabaali will meet Nassimbwa at 9:20 A.M.
Explanation:
Step 1: Create an equation to represent Mbabaali's journey:
- Mbabaali starts at 7:30 A.M. and cycles towards Nassimbwa's house at a speed of 16 km/h.
- We know that distance = rate * time (i.e., d = rt)
Since he cycles at a speed of 16 km/h, we can represent his distance (d) using the following equation:
dM = 16t
- Note that t represents the amount of time it takes Mbabaali to cycle.
Step 2: Create an equation to represent Nassimbwa's journey:
- Nassimbwa starts at 8:00 A.M. and cyles twoards Mbabaali's house at a speed of 8 km/h.
- We're told that she cycles 30 minutes later than Mbabaali (i.e., 0.5 hours.
Since she cycles at a speed of 16 km/h and 0.5 hours later than Mbabaali, we can represent her question using the following equation:
dN = 8(t - 0.5)
Step 3: Determine the sum of Mbabaali and Nassimbwa's distances:
- The sum of their distances equals the total distance between them (40 km).
Thus, we can represent this with the following equation:
dM + dN = 40
Step 3: Substitute the expressions for dM and dN and solve for t:
Now we can find time by substituting 16t for dM and 8(t - 0.5) for dN:
40 = 16t + 8(t - 0.5)
40 = 16t + 8t - 4)
(40 = 24t - 4) + 4
(44 = 24t) / 24
11/6 = t
Thus, the time it takes Mbabaali to cycle is 11/6 hours.
Step 4: Convert the 11/6 hours to minutes:
To convert 11/6 hours to minutes, we can multiply it by 60 since there are 60 minutes in 1 hour:
Mbabaali's cycling time in minutes = 11/6 hours * 60 minutes
Mbabaali's cycling time in minutes = 110 minutes
Thus, it takes Mbabaali 110 minutes to cycle
Step 5: Determine when Mbabaali and Nassimbwa will meet:
Since Mbabaali started at 7:30 A.M., the pair will meet 110 minutes after 7:30 A.M.:
Meeting time = 7:30 A.M. + 110 minutes
Meeting time = 9:20 A.M.
Thus, Mbabaali will meet Nassimbwa at 9:20 A.M.