A matatu left Nyahururu town at 6:15am and travelled towards Nairobi at an average speed of 96km/h.At the same time another matatu left Nairobi and headed for Nyahururu at an average speed of 84km/h.If the distance between Nairobi and Nyahururu is about 180km,Calculate:
a)The time they meet,
b) How far the matatu that left Nyahururu was from when they meet.
To solve this problem, we can use the formula: distance = speed * time.
Let's say t is the time it takes for the matatus to meet.
a) The time they meet:
The distance covered by the matatu that left Nyahururu is 96t km.
The distance covered by the matatu that left Nairobi is 84t km.
Since the total distance between Nairobi and Nyahururu is 180 km, we can set up the equation:
96t + 84t = 180
Simplifying the equation, we have:
180t = 180
Dividing both sides by 180, we get:
t = 1
Therefore, the matatus meet after 1 hour, or at 7:15 am.
b) How far the matatu that left Nyahururu was from when they meet:
Using the equation we derived in part a), we can substitute t = 1 to find the distance.
Distance = 96 * 1 = 96 km
Therefore, the matatu that left Nyahururu was 96 km away from the meeting point.