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/hour faster than five times the average speed of the bus. What is the average speed of the bus?

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Answer 1 · 2015-09-05T09:43:42

The speeds are:
Bus: 40 km/h
Plane: 320 km/h

Let's start with the symbols:

Let #D# be the distance covered by both vehicles, #B# the speed of the bus, #P# the speed of the plane.

From the first sentence we can figure out, that:

#B=D/12# and #P=D/1.5#. (1)

The second sentence shows us the relation between #P# and #B#

#P=120+5B# (2)

If we substitute #B# and #P# from (1) in (2) we get the equation with #D# only, so we can calculate #D#

#D/1.5=5*D/12+120#

We multiply both sides by 12.

#8D=5D+1440#
#3D=1440#
#D=480#

The distance is 480 km.
Now we can calculate both speeds:

#B=480/12=40# km/h

#P=480/1.5=320# km/h