Math help?

Question

a bus takes 12 hours to travel the same distance that an airplane travels in 1.5 hours. The average speed of the airplane is 120 km per hour faster than five times the average speed of the bus. What is the average speed of the bus?

Answer 1

You will need to conduct a chart :

_ _Rate_____Time_____Distance__
Bus X 12 12x
-------------------------------------------------------
Airplane 5n + 120 1.5 7.5x + 180
__________________________________



12n = 7.5x + 180

4.5x = 180

x = 40

The bus travels at 40 km/h

Answer 2

Let A = the speed of the airplane
Let B = the speed of the bus

The distance is the same:
D = 12 * B
D = 1.5 * A

Then you also know a relationship between A and B:

A = 120 + 5B

So plug this into the second equation, equate the two and solve.

D = 1.5A
D = 1.5(120 + 5B)
D = 180 + 7.5B

We also know from the first equation that:
D = 12B

So equate the two:
12B = 180 + 7.5B

Subtract 7.5B from both sides:
4.5B = 180

Divide both sides by 4.5:
B = 180 / 4.5
B = 40 kph

(For fun, you can figure the speed of the airplane. It is 120 + 5B = 120 + 5(40) = 320 kph. And as a double-check, compute D. D = 12B = 480km. The plane goes 320km in 1 hour, and 480km in 1.5 hours. So our answer checks out.)

The speed of the bus is 40 kph.

Answer 3

120+ 5x = 8x where x is the speed of the bus . So 3x = 120 and x = 40. Et voilà.

Answer 4

let the speed of the bus be x kmph
speed of the plane=5x+120
12x=(3/2)(120+5x)
multiplying by 2/3
8x=120+5x
adding -5x
3x=120
dividing by 3
x=40
speed pf the bus=40 kmph
speed of the plne=320 kmph

Answer 5

Let x= rate of bus, 5x+120=rate of plane

distances are the same

12x=1.5(5x+120)
12x=7.5x+180
4.5x=180
x=40

40mph

Answer 6

a=120+5b

x/b=12
12b=x
x/a=1.5
1.5a=x
12b=1.5a
a=8b=120+5b
3b=120
b=40 kph bus
a=120+5b=120+5*40=320 kph air
x=12*40=480km distance

Answer 7

distance = rate*time
d= 12*b
d= 1.5*a

a = 5b+120

12b = 1.5a
12b =1.5(5b+120)
12b = 7.5b + 180
4.5b = 180
b = 40 km/hr

Answer 8

40 KM