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# Please help me. Just this 2 questions very hard for me. I'm just not good at word problems.?

1. 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? Let x represent the speed of the bus.

2. A painting is 3 inches longer than it is wide. It is set in a rectangular border that is 2 inches wider than the painting on each side. If the area of the border is 100 in2, what are the dimensions of the painting?

Thanks so much.

If you know the answer please tell me, I'd greatly appreciate it.

Please show me an equation on the problems if possible so I can understand. Also help to solve the equation. Thanks.. :-)

Relevance

Airplane is 12/1.5 = 8 times faster than the bus.

Speed of bus is x.

Speed of plane is 120 km per hour faster than five times the average speed of the bus,

so speed of plane is 5x + 120

but speed of plane is also 8x.

So, 8x = 5x+120

3x = 120

x = 40

So speed of bus is 40 km/h

2) Let the height of the painting be h. The width is h+3

The area of the border is given as 100, but we can work it out

in terms of h by splitting it into 4 sides:

2*h + 2*h + 2*(h+3) + 2*(h+3)

Now add the 4 corners of the border, each 2*2=4,

so total of 16.

Border area = 4h + 4(h+3) + 16

But border area is also 100

so 4h + 4(h+3) + 16 = 100

simplify

4h + 4h + 12 + 16 = 100

8h + 28 = 100

8h = 72

h = 9

So height = 9 inches

And it's 3 inches longer than it is wide, so width=12 inches

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• 1. Let's take out the important parts:

- A bus takes 12 hours to travel distance an airplane could in 1.5 hours. That means the airplane is 12/1.5 = 8 times faster than the bus.

- The average speed of an airplane is 120km faster than five times the average of a bus. This one's a long sentence, so let's start using algebra:

Let the speed of the bus be x (miles/hour), then the airplane's average speed would be 5x+120 (miles/hour). Now that you've gotten the speed of the airplane in x, let's look back at the first statement: Airplane's speed is 8 times faster than bus's speed, putthing those two together:

8x = 5x + 120

Subtracting 5x from both sides: 3x = 120

Dividing 3 from both sides: x = 40

2. Again, take out what you know from the question:

- This painting is rectangular, with width x inches and length x+3 inches.

- The painting has a border which is 2 inches wider on each side. Remember that length and width has two sides(left/right, and top/bottom), so in total the length and width of the border is 4 inches longer than the picture's length and width respectively. That means length of border

= x+3+4

= x+7 inches

And width of border

= x+4 inches

- The area of the border is 100 in2. The area of the border is basically length*width MINUS the area of the picture. So you have your equation there:

(x+7)(x+4) - x(x+3) = 100

x^2 + 11x + 28 - x^2 - 3x = 100

8x + 28 = 100

8x = 72

x = 9

Width of painting = 9 inches

Length of painting = 9 + 3 = 12 inches.

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• Question 1 :

v = d/t (distance over time)

d = vt

"A bus takes 12 hours to travel the same distance that an airplane travels in 1.5 hours"

distance bus = distance air plane

vt = vt

12X = 1.5Y (let Y be the speed of the airplane)

Y = 8X

"The average speed of the airplane is 120 km per hour faster than five times the average speed of the bus"

Y = 120 + 5X

(now we have simultaneous equations!)

120 + 5X = 8X

120 = 3X

X = 40 km per hour

Question 2... I also don't understand. Sigh...

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• d=distance

va: speed of airplane

vb: speed of bus

va=120+5vb *

d=va*ta=vb*tb

va*1.5=vb*12 ; va=8vb **

by solving eq. * and ** 8vb=120+5vb ; vb=40 and va=8*40=320

excuse me I have not time to solve other one.

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