emilyy4757
27.11.2020 •
Mathematics
A train freight car weighs 25 tons when empty. A conveyor belt pours coal into the car at a constant rate of 1/3 ton per minute until it is full.
The dump truck (Refer to problem 8) weighs 55 tons when filled. At the same time the freight car is being filled, an identical freight car filled
to capacity is being emptied at a rate of 1/6 ton per minute.
How long, in minutes, until the freight cars are the same weight?
The tucks will weigh the same in
minutes.
How much coal will be in each truck when they weigh the same?
There will be
tons of coal in each truck.
Solved
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Ответ:
Step-by-step explanation:
Step one:
mass of Freight car=25tons
the rate of filling is 1/3 ton per minute
let the time taken to fill the freight car be x
and the total mass after x minute be y
Hence the mass as a function of time is expressed as
y=25+1/3x1
mas of dump truck=55tons
rate of being emptied= 1/6 tons per minute
let the time taken to empty the dump truck be x
and the total mass after x minute be y
Hence the mass as a function of time is expressed as
y=55-1/6x2
Step two:
equating equations 1 and 2,
1. The tucks will weigh the same in
55-1/6x=25+1/3x
collect like terms
55-25=1/3x+1/6x
30=(2+1/6)x
30=3/6x
30=1/2x
30=0.5x
x=30/0.5
x=60min
or
1 hour
The tucks will weigh the same in 60minutes(1 hour)
2. How much coal will be in each truck when they weigh the same?
For the train freight car, the weight after 60 minutes is
y=25+1/3(60)
y=25+20
y=55tons
55-25=20tons
There will be 20tons
For the dump truck, the weight after 60 minutes is
y=55-1/6(60)
y=55-10
y=45tons
55-45=10tons
There will be 10tons
Ответ: