Mathematics, 28.08.2019 09:30 sandrafina2004

Abus goes from town a to b in an exact time. if the bus goes at the rate of 50km/h, then it will arrive b 42min later than it had to and if it increases its speed 5.5/9 m/sec., it will arrive b 30min earlier. find:
a) the distance between the two towns;
b) the exact time that it takes to arrive town b
c) the speed of the bus(by schedule) for the exact time.

Answers: 2

Show answers

Answers

Answer from: jj11vb

Let the speed of bus for the exact time = x km/h
the distance between the cities = y km
then the exact time would be, t hours = (y/x) hours

If the bus goes at the rate of 50km/h, then it will arrive B 42min later,
speed = 50 km/h
42 minutes = 42/60 hours = 7/10 hours = 0.7 hours
time taken = t+0.7
distance = speed×time
⇒ y = 50×(t+0.7)
⇒ y = 50t + 35 (1)

it increases its speed 5.5/9 m/sec, it will arrive B 30min earlier.
5.5/9 m/s = (5.5/9)×(18/5) km/h = 2.2 km/h
30 minutes = 30/60 = 0.5 hour
speed = (x+2.2) km/h
time = (t - 0.5) hours

distance = speed×time
⇒ y = (x+2.2)×(t-0.5)
⇒ y = ((y/t) +2.2)×(t-0.5) (t = y/x)
⇒ y = y - 0.5 (y/t) + 2.2t - 1.1
⇒ 0.5 (y/t) - 2.2t + 1.1 = 0   (subtracting y from both sides)
⇒ (y/t) - 4.4t - 2.2 = 0    (dividing both sides by 0.5)
⇒ y - 4.4t² - 2.2t = 0    (multiplying both sides by t)
⇒ 50t + 35 - 4.4t² - 2.2 t = 0 (from equation 1)
⇒ -4.4t² + 35 + 47.8t = 0
⇒ 4.4t² - 47.8t - 35 = 0

solving the quadratic equation, we get t = 11.55 hours
y = 50t + 35 = 612.5 km
x = 612.5/11.55 = 53 km/h

A) 612.5 km
B) 11.55 hours
C) 53 km/h

Answer from: JayJay9439

The Logic Defined:

1 Minute=t, (a unit of time)

Time (By schedule)=nt, (n>0), nt=number of minutes

Metre(s)=m

Speed=s (in metres per minute), s=[distance in metres]/[time in minutes]

Distance=d (in metres), d=[speed in metres per minute]*[time in minutes]

---------------------------------------------

Statement (1):

"If the bus goes at the rate of 50km/h, then it will arrive B 42min later than it had to."

Conclusion 1:

$\frac { 50km }{ h } =\frac { 50,000m }{ 60t } =\frac { 2,500m }{ 3t } \\ \\ \therefore \quad \frac { 2,500m }{ 3t } =nt+42t\\ \\ \frac { 2,500m }{ 3t } =t\left( n+42 \right)$

$\\ \\ 2,500m=3{ t }^{ 2 }\left( n+42 \right) \\ \\ m=\frac { 3{ t }^{ 2 }\left( n+42 \right) }{ 2,500 }$

Statement (2):

"if it increases its speed 5.5/9 m/sec., it will arrive B 30min earlier."

Conclusion 2:

$\frac { 5.5m }{ 9\quad seconds } =\frac { 5.5m }{ \frac { 9 }{ 60 } t } =\frac { 110m }{ 3t }$

$\\ \\ \therefore \quad \frac { 110m }{ 3t } =nt-30t\\ \\ \frac { 110m }{ 3t } =t\left( n-30 \right) \\ \\ 110m=3{ t }^{ 2 }\left( n-30 \right)$

$\\ \\ m=\frac { 3{ t }^{ 2 }\left( n-30 \right) }{ 110 }$

Conclusion 3, because of conclusion 1 and 2:

$\frac { 3{ t }^{ 2 }\left( n-30 \right) }{ 110 } =\frac { 3{ t }^{ 2 }\left( n+42 \right) }{ 2,500 } \\ \\ 7,500{ t }^{ 2 }\left( n-30 \right) =330{ t }^{ 2 }\left( n+42 \right) \\ \\ 7,500\left( n-30 \right) =330\left( n+42 \right)$

$\\ \\ 7,500n-225,000=330n+13,860\\ \\ 7,500n-330n=13,860+225,000\\ \\ 7,170n=238,860\\ \\ n=\frac { 238,860 }{ 7,170 } \\ \\ \therefore \quad n=\frac { 7962 }{ 239 }$

Therefore,

$Time\quad by\quad schedule=\frac { 7962 }{ 239 } t\\ \\ Approx:\quad 33.3\quad mins$

Now we want to find the distance between the two towns, so we say that:

$d=\frac { 2,500m }{ 3t } \cdot \left( \frac { 7962 }{ 239 } t+42t \right) \\ \\ =\frac { 2,500m }{ 3t } \cdot \frac { 18,000 }{ 239 } t$

$\\ \\ =\frac { 45,000,000 }{ 717 } m\\ \\ Approx:\quad 62,761.5\quad metres\\ \\ In\quad km\quad (approx):\quad 62.761\quad km$

So now you want to know how fast the bus has to travel to get to its destination on time...

Use the formula: s=d/t

Therefore:

$s=\frac { \frac { 45,000,000 }{ 717 } m }{ \frac { 7962 }{ 239 } t } \\ \\ Approx:\quad 1,883.9\quad metres\quad per\quad minute$

Answer from: Quest

5 1/4 miles per hour

step-by-step explanation:

15 3/4 / 3 = 5 1/4

Answer from: Quest

Ithink the answer is c

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Will give find an equivalent function to f(x)=5(2)^3x. the 5(2)^3x means 5(2) to the 3x power answer choices: a: f(x)=125^x(8)^x b: f(x)=10^2x c: f(x)=40^x d: f(x)=5(8)^x

Answers: 3

Answer

Mathematics, 21.06.2019 15:40

What is the first quartile of this data set? 10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38 a. 12 b. 19 c. 29 d. 10

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Describe a situation that you could represent with the inequality x< 17

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

Answers: 1

Answer

You know the right answer?

Abus goes from town a to b in an exact time. if the bus goes at the rate of 50km/h, then it will arr...

Questions

Mathematics, 05.11.2020 22:10

What is the factored form of x^-9...