Answer:
The distance travelled by bus is 281.25 km and the distance travelled by airplane is 1,618.75 km.
Step-by-step explanation:
Let's use b for bus and a for airplane
We know that distance = speed × time
The total distance is 1900 km
x + y = 1900
Average speed by bus = 60km/h or x/60 h
Average speed by plane = 700km/h or y/700 h
Total travelling time = 7h
So we write the equation as:
x/60 + y/700 = 7
First we need to solve for y in the equation x + y = 1900
x + y = 1900
Subtract x from both sides
x - x + y = 1900 - x
y = 1900 - x
Now that we have y, we can substitute y in the equation x/60 + y/700 = 7
x/60 + y/700 = 7
x/60 + 1900 - x / 700 = 7
And now we solve for x in the equation: x/60 + 1900 - x / 700 = 7
x/60 + 1900 - x / 700 = 7
Multiply both sides of the equation by 2100, the least common multiple of 60,700
35x + 3(1900 − x) = 14700
Use the distributive property to multiply 3 by 1900 − x
35x + 5700 − 3x = 14700
Combine 35x and −3x to get 32x
32x + 5700 = 14700
Subtract 5700 from both sides.
32x + 5700 - 5700 = 14700 − 5700
Subtract 5700 from 14700 to get 9000
32x = 9000
Divide both sides by 32.
32x/32 = 9000/32
Reduce the fraction 9000/32 to lowest terms by extracting and cancelling out 8.
x = 9000/32
x = 281.25
Now that we have x, we can solve for y in the equation: y = 1900 - x
y = 1900 - x
Substitute x with 281.25
y = 1900 - 281.25
Subtract 281.25 from 1900 to get
y = 1618.75
So, the distance travelled by bus is 281.25 km and the distance travelled by airplane is 1618.75 km.
