The distance between two towns A and B is360km.A minibus left town A at 8.15a.m and travelled towards B at an average speed of 90km/hr. A matatu left town B at 10.35a.m on the same day and travelled towards A at an average speed of 110km/hr.
a)i)how far from A did they meet? (4mk)
10:35-8:15 = 2:20 = 2.33 h. delay.
90T + 110(T-2.33) = 360
200T-256 = 360
T = 3.08 h.
d = 90 * 3.08 = 277 km from Town A.
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I like the method
The distance that the minibus covered before the matatu started the journey is 10:35-8:15 which gives 2hrs&20min. So the distance is 2.333333333 times 90km/hr which gives 210km. Therefore relative distance is 360-210 which gives 150km . while relative speed is 110 plus 90km/h, which gives 200km/hr . but relative time is equal to relative distance divide by relative speed which is 150km divide by 200 , which gives 45 min or 3/4hrs . this is the time they took to meet .but distance they covered to meet from A is 3/4 times90km/hr which gives 67.5.which we add to 210 which gives 277.5 which is the answer
To find the distance from town A where the two vehicles meet, we need to calculate the total distance covered by each vehicle until they meet.
First, let's calculate the time taken by the minibus to reach the meeting point.
The minibus started at 8.15 a.m. and traveled at an average speed of 90 km/hr. To calculate the time taken, we can use the formula:
Time = Distance / Speed
The distance traveled by the minibus in this time period is:
Distance = Speed x Time = 90 km/hr x (time taken by the minibus)
The time taken by the minibus is the difference between the time it started and the time the matatu left town B:
Time taken by the minibus = 10.35 a.m. - 8.15 a.m.
Convert the time into fractions of hours:
Time taken by the minibus = 2 hours 20 minutes = 2.33 hours
Now, let's calculate the distance covered by the minibus:
Distance = 90 km/hr x 2.33 hours
Next, let's calculate the time taken by the matatu to reach the meeting point.
The matatu left town B at 10.35 a.m. and traveled at an average speed of 110 km/hr. To calculate the time taken, we can use the same formula:
Time = Distance / Speed
Since the matatu started after the minibus, we need to calculate the time difference:
Time taken by the matatu = Time taken by the minibus + Time difference
Time difference = (10.35 a.m. - 8.15 a.m.) - 2.33 hours
Convert the time into fractions of hours:
Time difference = 2 hours 20 minutes - 2.33 hours
Now, let's calculate the distance covered by the matatu:
Distance = 110 km/hr x (Time taken by the minibus + Time difference)
The meeting point will be the sum of the distances covered by the minibus and the matatu.
Meeting point = Distance covered by the minibus + Distance covered by the matatu
Substituting the values, we can calculate the distance from town A where they meet.