Complete the following problems. Please show your work. 1. A freight train leaves the station traveling due north at a speed of 40 mph. One hour later, a passenger train leaves the same station traveling due north on a parallel track at a speed of 50 mph. How long will it take the passenger train to overtake the freight train?

2. The width of a soccer field recommended for players under 12 is 32 yards less than the length. The perimeter of the fields is 290 yards. Find the dimensions of the field.

3. Jeanette can be paid in one of two ways for painting a house. : Plan A; $100 plus $15 per hour; Plan B: $25 per hour. Suppose that a job takes n hours to complete. For what values of n is Plan is Plan A better for Jeanette?

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Step-by-step explanation:

(1)

Using the relationship

distance (d) = speed (s) × time (t)

The freight train leaves the station 1 hour earlier than the passenger train, so

d = 40(t + 1) ← Freight train

d = 50t ← Passenger train

We require to find when they are at the same distance from the station, then equating the 2 equations

50t = 40(t + 1) ← distribute

50t = 40t + 40 ( subtract 40t from both sides )

10t = 40 ( divide both sides by 10 )

t = 4

The passenger train will overtake the freight train after 4 hours

(2)

let l represent length, then width = l - 32

perimeter (P) = 2l + 2w = 290, that is

2l + 2(l - 32) = 290 ← distribute and simplify left side

2l + 2l - 64 = 290

4l - 64 = 290 ( add 64 to both sides )

4l = 354 ( divide both sides by 4 )

l = 88.5 and w = 88.5 - 32 = 56.5

Then dimensions are 88.5 yards by 56.5 yards

(3)

Plan A : 100 + 15n

Plan B : 25n

When is Plan A better than Plan B , that is

100 + 15n > 25n ( subtract 25n from both sides )

100 - 10n > 0 ( subtract 100 from both sides )

- 10n > - 100

Divide both sides by - 10, reversing the symbol as a result of dividing by a negative quantity.

n < 10

Plan A is better when number of hours (n) is less than 10

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