A Matatu left Nairobi a 7.00 Am for Kisumu at an average speed of 75km/h. A car also left Nairobi 40 minutes later for Kisumu along the same route at an average speed of 105 km/h (a) Determine (i) The time when the car caught up with the matatu (ii) the distance from nairobi when the car caught up with the matatu
the speed difference is 30 km/hr
in 40 minutes, car A has gone 50 km.
(i) 50km ÷ 30km/hr = 5/3 hr -- you figure the time
(ii) 50 + 5/3 * 75 = 175 km = 105 * 5/3
To determine the time when the car caught up with the matatu, we can use the concept of relative speed. Relative speed is the difference in speeds between two moving objects traveling in the same direction.
Given data:
Speed of the matatu = 75 km/h
Speed of the car = 105 km/h
To determine the time when the car caught up with the matatu, we need to consider the head start the matatu had. The car left 40 minutes (or 40/60 = 2/3 hours) later than the matatu. So, when the car started, the matatu had already covered a distance of (75 km/h) * (2/3 hours) = 50 km.
Let's denote:
t = time taken by the car to catch up with the matatu
Now, let's set up an equation based on the relative speeds:
Distance covered by the car = Distance covered by the matatu + Head start distance
Using the formula: Distance = Speed * Time
(105 km/h) * t = (75 km/h) * t + 50 km
Simplifying the equation:
105t = 75t + 50
30t = 50
t = 50 / 30
t = 5/3 hours (or 1 hour and 40 minutes)
So, it took the car 1 hour and 40 minutes to catch up with the matatu.
To determine the distance from Nairobi when the car caught up with the matatu, we can substitute the value of t back into any of the earlier equations.
Let's use the equation:
Distance covered by the car = Speed of the car * Time taken by the car
Distance = (105 km/h) * (5/3 hours)
Distance = 175 km
Therefore, the car caught up with the matatu 175 km from Nairobi.
To determine the time when the car caught up with the matatu, we need to find the time it took for the car to cover the same distance as the matatu.
Let's start by finding out how long the matatu has been traveling when the car starts. The car left 40 minutes (or 40/60 = 2/3 hours) later than the matatu's departure time.
The matatu traveled for t hours, and the car traveled for (t - 2/3) hours.
Now, let's use the formula distance = speed × time to find the distance covered by each vehicle.
Distance covered by the matatu = 75 km/h × t hours
Distance covered by the car = 105 km/h × (t - 2/3) hours
When the car caught up with the matatu, they had covered the same distance. So we can set up the equation:
75t = 105(t - 2/3)
Let's solve for t:
75t = 105t - 70
30t = 70
t = 70/30
t ≈ 2.33 hours
(i) The time when the car caught up with the matatu is approximately 2.33 hours after the matatu's departure time. To convert this to minutes, we multiply by 60:
2.33 hours × 60 = 140 minutes
Therefore, the car caught up with the matatu after approximately 140 minutes.
(ii) To find the distance from Nairobi when the car caught up with the matatu, we substitute t = 2.33 back into the distance formula for the matatu:
Distance = 75 km/h × 2.33 hours
Distance ≈ 175.5 km
Therefore, the car caught up with the matatu when they were approximately 175.5 km away from Nairobi.