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Misha Larkins [42]
2 years ago
11

At 1:00 p.m. a car leaves st. louis for chicago, traveling at a constant speed of 65 miles per hour. at 2:00 p.m. a truck leaves

chicago for st. louis, traveling at a constant speed of 55 miles per hour. if it is a 305-mile drive between st. louis and chicago, at what time will the car and truck pass each other?
Mathematics
1 answer:
Maurinko [17]2 years ago
8 0
Let x =  miles traveled by car
Let y = miles traveled by truck.

Because the total distance is 305 miles,
x + y = 305       (1)

Let t = hours of travel by truck. Because the truck speed is 55 mph,
55*t = y            
or 
t = y/55              (2)

The car has an hour head start, therefore it travels for (t + 1) hours.
Because the car travels at 65 mph,
65*(t + 1) = x
Substitute (2) to obtain
65*(y/55 + 1) = x
or
1.1818y + 65 = x        (3)

From (1), obtain
1.1818y + 65 = 305 - y
2.1818y = 240
y = 110
x = 305 - y = 195

From (2),
t = 110/55 = 2 hours

The two vehicles pass each other at 2:00 pm + 2 hours  = 4:00 pm

Answer: 4:00 pm
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Answer:

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Step-by-step explanation:

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The mean of the exponential

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Now the probability we need

p[T<5] = ₀∫⁵ t(t) dt

=₀∫⁵ 1/8×e^-t/8 dt

= 1/8 ₀∫⁵ e^-t/8 dt

= 1/8 [ (e^-t/8) / -1/8 ]₀⁵

= - [ e^-t/8]₀⁵

= - [ e^-5/8 - 1 ]

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<u></u>

b)

Now we find t such that;

p[T>t] = 0.95

so

t_∫¹⁰ t(x) dx = 0.95

t_∫¹⁰ 1/8×e^-x/8 = 0.95

1/8 t_∫¹⁰ e^-x/8 dx = 0.95

1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t  = 0.95

- [ e^-x/8]¹⁰_t = 0.96

- [ 0 - e^-t/8 ] = 0.95

e^-t/8 = 0.95

take log of both sides

log (e^-t/8) = log (0.95)

-t/8 = In(0.95)

-t/8 = -0.0513

t = 8 × 0.0513

t = 0.4104 (min)

so we convert to seconds

t = 0.4104 × 60

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Answer: 15.7 minutes

Step-by-step explanation:

Let x be the time in the beginning (in minutes).

Given: The track team is trying to reduce their time for a relay race.

First they reduce their time by t_1=2.1 minutes.

Then they are able to reduce that time by t_2=10

If their final time is 3.96 minutes, then

x-t_1-t_2=3.6\\\Rightarrow\ x=3.6+t_1+t_2\\\Rightarrow\ x=3.6+2.1+10\\\Rightarrow\ x= 15.7

Hence, their beginning time was 15.7 minutes.

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Answer:

45 segundos.

Step-by-step explanation:

Un tren pasa por delante de un puente en 15 segundos; si el puente tuviera el doble de longitud, le tomaría el doble de tiempo en cruzarlo, si tuviera el triple de longitud, le tomaría el triple de tiempo y así sucesivamente.

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