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nataly862011 [7]
3 years ago
9

Two jet planes simultaneously started travelling in opposite directions from the same airport. Four hours later they were 3800 m

iles apart. If one plane traveled 80 miles per hour faster than the other, what was the speed of each plane?A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets him to the top travelling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Mathematics
1 answer:
alexira [117]3 years ago
8 0

Answer:

Step-by-step explanation:

let the speed of one plane=x

speed of other plane=x+80

time=4 hrs

then 4x+4(x+80)=3800

4x+4x+320=3800

8x=3800-320

or 8x=3480

x=435

speed of one plane=435 m/h

speed of other plane=435+80=515 m/h

2.

Let he walks x hrs

then he take a taxi for 2-x hrs

4x+(2-x)50=31

4x+100-50x=31

-46x=-69

x=\frac{-69}{-46}=\frac{3}{2}

so he walks 3/2 hrs=1.5 hrs

travels by taxi=2-1.5=0.5 hrs

distance traveled by taxi=0.5×50=25 miles

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Hi,

\sqrt{200}  = 14.14

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r3t40
3 0
3 years ago
Solve the system by substitution.<br> - 2x – 10y = -2<br> -4y = x
mihalych1998 [28]

Answer:

x = -4 and y = 1

Step-by-step explanation:

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4 0
3 years ago
Carson needs to lease out a music studio to record his new album. The studio charges an initial studio-use fee plus an hourly fe
Naily [24]

Answer:

The y-intercept of the equation is 100 and represents the initial studio-use fee.

Step-by-step explanation:

In this equation, our t variable (time) is the equivalent of the x-variable on a graph. This is because it is the variable that we 'change' to see its impact on y. We see how the amount of hours affects the price. So our P variable (price) is the equivalent of y on a graph. The y-intercept is where the line crosses the y-axis on a graph. At this point, x=0.

Since P is our y, and t is our x, to find the y-intercept, we simply need to make t = 0.

P = 50(0) + 100

P = 100

Therefore the y-intercept is 100.

In this context, t represents time, so even though the studio has been used for 0 hours, the price is still 100. This is because the 100 represents the initial studio-use fee, and using it for certain amounts of time adds onto the initial fee of $100. The hourly fee is represented by 50t so it costs $50 more for each hour of use.

Hope this helped!

5 0
3 years ago
równanie zmiany prędkość autokaru poruszającego się po prostym odcinku szosy i rozpoczynającego hamowanie od szybkości 20m/s ma
Rasek [7]

Answer:

s = 22.5 m

Step-by-step explanation:

the equation for the speed change of a coach moving along a straight section of the road and starting braking at a speed of 20 m / s has the form v (t) = 25-5t. Using integral calculus, determine the coach's braking distance.

v (t) = 25 - 5 t

at t = 0 , v = 20 m/s

Let the distance is s.

s =\int v(t) dt\\\\s =\int (25 - 5t)dt\\\\s= 25 t - 2.5 t^2 \\

Let at t = t, the v = 20

So,

20 = 25 - 5 t

t = 1 s

So, s = 25 x 1 - 2.5 x 1 = 22.5 m

3 0
2 years ago
A tug boat traveled -15 miles in 0.3 hours what was its velocity
GenaCL600 [577]

Answer:

22.35 m/s

Step-by-step explanation:

The distance is always a positive unit, so distance traveled (d) = 15 miles

Time (t) = 0.3 hours

Time (t) = 0.3 * 60 = 18 minutes

(1 hour = 60 minutes)

Velocity (v) = ?

The formula of distance is: d = v*t

=> v = d/t = 15/18 = 0.83 miles/minute

we can also calculate velocity is meter/sec, for that

1 minute = 60 sec

=> 18 mins = 18*60 = 1080 sec

1 mile = 1609.34 meters

=> 15 miles = 15 * 1609.34 = 24,140 m

hence,

v = 24,140/1080 = 22.35 m/s

4 0
3 years ago
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