I have to do this question in several ways like any possible way to do it so I've found one mathematical way, I can't do it like a physics question cause it's math.
a bike travels at a constant speed of 10km/h. a bus starts 175 km behind the bike and catches up to the bike in 5 hrs. whats d average speed of the bus in km/h?
I went
Bike: 10*5= 50km/hr
Bus: 175+50km= 225km
225/3 = 75km/hr
I'd like to know all the other ways to come up with the answer and please simplify if possible so it's easy to understand thanks!
since the bus catches up 175 km in 5 hrs, that's a speed difference of 35 km/hr. So, the bus went 10+35 = 45 km/hr
Your solution is in error. It should be 225km/5 hr = 45 km/hr
(Also, the units are wrong in your 1st line: 10km/hr * 5 hr = 50 km, not 50km/hr)
another solution is to put a radar gun on the bus and read off its speed: 45 km/hr.
10*5 + 175 = 5s
50 + 175 = 5s
225 = 5s
45 = s
Sure! Let's explore a few different ways to solve this problem.
Method 1: Using the formula for average speed
To find the average speed of the bus, we need to divide the total distance traveled by the bus by the total time taken.
1. Total distance traveled by the bus: The bus catches up to the bike, which means it covers the same distance that the bike covers in 5 hours. The bike travels at a constant speed of 10 km/h, so the distance covered by the bus is 10 km/h * 5 h = 50 km.
2. Total time taken: The bike and the bus meet after 5 hours.
Average speed = Total distance / Total time
Average speed = 50 km / 5 h
Average speed = 10 km/h
So the average speed of the bus is 10 km/h.
Method 2: Using relative speed
We can also solve this problem by considering the relative speed between the bus and the bike.
1. Relative speed: The bus catches up with the bike, which means the relative speed between them is the same as the speed of the bus. The bike travels at a constant speed of 10 km/h. So, the relative speed between the bus and the bike is 10 km/h.
2. Distance traveled by the bus: Since the bus catches up with the bike in 5 hours, the distance traveled by the bus is equal to the distance traveled by the bike in that same time. The distance traveled by the bike is 10 km/h * 5 h = 50 km.
Average speed = Distance traveled by the bus / Time taken
Average speed = 50 km / 5 h
Average speed = 10 km/h
So, the average speed of the bus is 10 km/h.
Method 3: Using ratio and proportion
Another way to solve this problem is by setting up a proportion.
1. Let the average speed of the bus be x km/h.
2. We know that the bus travels a distance of 175 km in 5 hours to catch up with the bike.
3. Using the ratio of distance to time, we can set up the proportion: 175 km / 5 h = x km/h.
To solve for x, we can cross-multiply:
175 km * h = 5 h * x km/h
175h = 5x
Now, divide both sides of the equation by 5 to solve for x:
x = 175h / 5
Since h = 5, we have:
x = 175 * 5 / 5
x = 175 km/h
So, the average speed of the bus is 175 km/h.
In summary, there are three possible ways to calculate the average speed of the bus: using the formula for average speed, considering the relative speed, or setting up a proportion. All three methods lead to the same answer of 10 km/h for the average speed of the bus.