Have world problem and I don't get it please explain step by step simplify and show me as many ways as possible cause one might be easier than other !!
A bicycle travels at constant speed of 15km/hr. Bus starts 195km behind bicycle and catches up to bicycle in 3 hrs. What's average speed of bus in km/hr????
They both travel for time t = 3 hours
the bike goes:
d = 15 t
the bus goes
d + 195 = v t
so
d = v t - 195
but t = 3 so
15(3) = v(3) - 195
45 = 3 v - 195
3 v = 240
v = 80 km/h
or, you can look at it like this. The bus makes up 195km in 3 hours, so it is going 195/3 = 65 km/hr faster than the bike.
15+65 = 80 km/hr
To solve this problem, we can break it down into several steps:
Step 1: Understand the problem.
We are given the speed of the bicycle and the distance between the bicycle and the bus when the bus starts. The bus catches up to the bicycle after 3 hours. We need to find the average speed of the bus.
Step 2: Define the variables.
Let's assign the following variables:
- Speed of the bicycle = 15 km/hr
- Distance between the bicycle and the bus = 195 km
- Time it takes for the bus to catch up = 3 hours
- Average speed of the bus = unknown (we'll solve for this)
Step 3: Calculate the distance the bicycle travels in 3 hours.
Since the bicycle travels at a constant speed of 15 km/hr, the distance it travels in 3 hours can be found by multiplying its speed by the time:
Distance = Speed * Time
Distance = 15 km/hr * 3 hrs
Distance = 45 km
Step 4: Calculate the speed of the bus.
The bus catches up to the bicycle after 3 hours, which means it also traveled a distance of 45 km in the same time. To find the average speed of the bus, we divide the distance traveled by the time taken:
Speed of the bus = 45 km / 3 hrs
Speed of the bus = 15 km/hr
Therefore, the average speed of the bus is 15 km/hr.
Alternative approach:
Another way to solve this problem is to use the concept of relative speed.
Step 1: Calculate the relative speed.
The relative speed between the bus and the bicycle can be found by subtracting the speed of the bicycle from the speed of the bus:
Relative Speed = Speed of the bus - Speed of the bicycle
Relative Speed = (Unknown bus speed) - 15 km/hr
Step 2: Use the formula Distance = Speed * Time to determine the relative distance between the bus and the bicycle.
The bus catches up to the bicycle in 3 hours, so the relative distance is the product of the relative speed and the time it takes to catch up:
Distance = Relative Speed * Time
Distance = (Unknown bus speed - 15 km/hr) * 3 hrs
Distance = (3 * (Unknown bus speed - 15)) km
Step 3: Since we know the relative distance is equal to the distance between the bus and the bicycle (195 km), we can equate these two distances and solve for the unknown bus speed.
195 km = 3 * (Unknown speed of the bus - 15 km/hr)
65 km = Unknown speed of the bus - 15 km/hr
Step 4: Solve for the unknown speed of the bus.
Adding 15 km/hr to both sides of the equation:
Unknown speed of the bus = 65 km + 15 km/hr
Unknown speed of the bus = 80 km/hr
So, the average speed of the bus is 80 km/hr.