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The speed of a freight train is 15ph slower that the speed of a passenger train

Math Sep 08, 2020

The speed of a freight train is 15ph slower that the speed of a passenger train. The freight train travels 390 mi in the same time that it takes the passenger train to travel 480 mi. Find the speed of each train.

It takes 60 oz of grass seed to seed 3000ft^2 of lawn. At the rate how much would be needed to seed 5000ft^2 of lawn?

Expert Solution

The speed of the freight train: x
the speed of the passenger train is therefore x+15

The time it takes an object traveling with speed v to travel distance D is:

t = D/v

Hence the time it takes the freight train to travel 390 miles is:

t = 390/x

And the time it takes the passenger train to travel 480 miles is:

t= 480/(x+15)

Since the two times are the same we have:

390/x = 480/(x+15)

390(x+15) = 480x

39x+39*15 = 48x

585 = 9x

x = 65mph

The speed of the freight train is x=65mph
The speed of the passenger train is x+15=80mph

Let u be the amount needed to seed 5000 sf of lawn.
the ratio of seeds to square foot is constant.

hence:

60/3000 = u/5000

60/3 = u/5

20 = u/5

100 = u

To seed 5000 sf of lawn we will need u=100oz of grass seeds.

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