Question 132273: A truck loaded with vegetables left Station B at 5:00 am and traveled eastward towards town M running at an average speed of 30 kph. At the same time, an express
bus left Station A, 30 km west of Station B, and traveled eastward towards town M
running at an average speed of 50 kph. When will the bus overtake the truck?
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! Your question is:
A truck loaded with vegetables left Station B at 5:00 am and traveled eastward towards town M running at an average speed of 30 kph. At the same time, an express bus left Station A, 30 km west of Station B, and traveled eastward towards town M running at an average speed of 50 kph. When will the bus overtake the truck?
This is a distance word problem. So, we can use the distance formula D = rt, where d = distance, r = rate or speed and t = time, in hours NOT MINUTES.
The best thing to do is to set up table.
Since the truck and bus are going in the same direction, distances are equal, obviously.
We know the speed of the truck and bus but we do NOT know the time. This is what we are searching for. So, let x represent time of vehicles in hours.
Truck Data:
time = x
rate = 30
Distance = 30x
==============
Bus Data:
time = x
rate = 50
distance = 50x
Here is where it gets tricky.
The question says: "At the same time, an express bus left Station A, 30 km west of Station B..."
That statement is saying that the truck is 30 km ahead of the bus.
Another way to look at this statement is to say that the bus is 30 km behind the truck also coming from the West heading East.
50x - 30 = distance of bus MINUS 30 km behind the truck
30x = truck distance
Equate and solve for x.
50x - 30 = 30x
50x - 30x = 30
20x = 30
x = 30/20
x = 3/2
What is 3/2 in terms of hours?
It is 1.5 hours or 1 hour and 30 minutes.
When will the bus overtake the truck? It will overtake the truck in 1 hour and 30 minutes.
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