A bus leaves town X at 1200 h for town Y at a speed of 64km/h. At the same time another bus leaves town Y for town X travelling at a constant speed of 60 km/h. Given that the distance between the two towns is 186 km,draw a distance _time graph showing both journeys and from your graph find when and where the buses pass each other
v = speed
s = distance
t = time
speed = distance / time
v = s / t
s = v • t
For first bus:
s1 = 64 t
For second bus:
s2 = 60 t
When the buses meet, the total length will be:
s1 + s2 = 186 km
64 t + 60 t = 186
124 t = 186
t = 186 / 124 = 62 • 3 / 62 • 2 =
3 / 2
t = 3 / 2 h = 1.5 h = 1h 30 min
12:00h + 1h 30 min= 13h 30 min =
13:30
Well, it's time to get creative and draw a comical distance-time graph for these two buses going on their little adventure!
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12:00 T(Bus Y): 4:00
This imaginative graph represents the journey of both buses. The horizontal axis represents time, and the vertical axis represents distance.
As you can see, the graph starts at 12:00 when both buses depart from their respective towns, X and Y. Bus X, traveling at 64 km/h, steadily gains distance from Y. Meanwhile, Bus Y, cruising at a not-so-speedy 60 km/h, tries its best to catch up. However, the two buses eventually meet at a point where their distances intersect.
Using this creative graph, it can be estimated that the buses pass each other at around 4:00.
Please keep in mind that this is a humorous and imaginative interpretation of the journey, so take it with a grain of clownish salt!
To draw a distance-time graph for the two bus journeys, we need to consider the time it takes for each bus to reach a specific distance.
Let's assume the time taken by the first bus (leaving town X) is "t" hours, and the time taken by the second bus (leaving town Y) is also "t" hours.
For bus 1:
Distance = Speed × Time
Distance = 64 × t
For bus 2:
Distance = Speed × Time
Distance = 60 × t
Since the distance between the two towns is 186 km, we can set up an equation:
64t + 60t = 186
By solving this equation, we can find the value of "t":
124t = 186
t = 186 / 124
t ≈ 1.5 hours
Now, let's calculate the distances covered by each bus after 1.5 hours.
For bus 1:
Distance = Speed × Time
Distance = 64 × 1.5
Distance ≈ 96 km
For bus 2:
Distance = Speed × Time
Distance = 60 × 1.5
Distance ≈ 90 km
Based on the calculations, after 1.5 hours, the first bus would have reached approximately 96 km, and the second bus would have reached approximately 90 km.
To draw the distance-time graph:
- The x-axis represents time (in hours).
- The y-axis represents distance (in kilometers).
We can plot the following points on the graph:
(0, 0) -> Starting point for both buses
(1.5, 96) -> First bus after 1.5 hours
(1.5, 90) -> Second bus after 1.5 hours
The graph will be a straight line from the origin (0,0) to these plotted points.
To find when and where the buses pass each other, we can determine the distance traveled by each bus at the time of passing.
Since both buses are traveling towards each other, the sum of the distances traveled by the two buses will be equal to the distance between the towns (186 km) when they pass each other.
Let's assume the time they pass each other is "t1" hours.
For bus 1:
Distance = Speed × Time
Distance1 = 64 × t1
For bus 2:
Distance = Speed × Time
Distance2 = 60 × t1
Since Distance1 + Distance2 = 186 km, we can set up another equation:
64t1 + 60t1 = 186
By solving this equation, we can find the value of "t1":
124t1 = 186
t1 = 186 / 124
t1 ≈ 1.5 hours
Therefore, the buses pass each other after approximately 1.5 hours. At that time, the first bus has traveled 96 km, and the second bus has traveled 90 km.
To draw a distance-time graph showing both journeys, we need to plot the distance traveled by each bus at different points in time.
Let's start by defining some variables:
- Bus X leaves town X at 1200 h.
- Bus Y leaves town Y at 1200 h.
- The speed of Bus X is 64 km/h.
- The speed of Bus Y is 60 km/h.
- The distance between the two towns is 186 km.
Now, let's calculate the time it takes for each bus to reach the point of intersection:
- Let's assume the buses meet after t hours.
- So, the time taken by Bus X to reach the intersection is t hours.
- The time taken by Bus Y to reach the intersection is also t hours.
To find when and where the buses pass each other, we can set up an equation using the distance formula: distance = speed × time.
For Bus X: distance_X = speed_X × time_X = 64t
For Bus Y: distance_Y = speed_Y × time_Y = 60t
Since the total distance between the towns is 186 km, the sum of the distances traveled by both buses will be equal to 186 km:
distance_X + distance_Y = 186
64t + 60t = 186
124t = 186
t = 1.5 hours (or 1 hour and 30 minutes)
Now, we can plot our distance-time graph:
- On the x-axis, we will represent time.
- On the y-axis, we will represent distance.
Bus X:
- At t = 0, distance_X = 0
- At t = 1.5, distance_X = 64 × 1.5 = 96 km
Bus Y:
- At t = 0, distance_Y = 0
- At t = 1.5, distance_Y = 60 × 1.5 = 90 km
From the graph, we can determine that the buses will pass each other 1.5 hours after they start, and the point of intersection will be 90 km from town X and 96 km from town Y.
Please note that the graph is not drawn here as this is a text-based platform, but you can easily plot it on a graph paper or using any graphing software.