1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
statuscvo [17]
3 years ago
9

Two automobiles left simultaneously from cities A and B heading towards each other and met in 5 hours. The speed of the automobi

le that left city A was 10 km/hour less than the speed of the other automobile. If the first automobile had left city A 4 1/2 hours earlier than the other automobile left city B, then the two would have met 150 km away from B. Find the distance between A and B.
Mathematics
2 answers:
Klio2033 [76]3 years ago
6 0

Answer:

450km

Step-by-step explanation:

Take it that each automobile travels at 30 km an hour, for 150 km, meaning it will be 450 km apart.

quester [9]3 years ago
5 0

Answer:

  450 km

Step-by-step explanation:

<u>Equations</u>

We can define 3 variables: a, b, d. Let "a" and "b" represent the speeds of the cars leaving cities A and B, respectively. Let "d" represent the distance between the two cities. We can write three equations in these three variables:

1. The relation between "a" and "b":

  a = b -10 . . . . . . . the speed of car A is 10 kph less than that of car B

2. The relation between speed and distance when the cars leave at the same time:

  d = (a +b)·5 . . . . . . distance = speed × time

3. Note that the time it takes car B to travel 150 km to the meeting point is (150/b). (time = distance/speed) The total distance covered is ...

  distance covered by car A in 4 1/2 hours + distance covered by both cars (after car B leaves) = total distance

  4.5a + (150/b)(a +b) = d

__

<u>Solution</u>

Substituting for d, we have ...

  4.5a + 150/b(a +b) = 5(a +b)

  4.5ab +150a +150b = 5ab +5b^2 . . . . . . multiply by b, eliminate parentheses

  5b^2 +0.5ab -150(a +b) = 0 . . . . . . . . . . subtract the left side

Now, we can substitute for "a" and solve for b.

  5b^2 + 0.5b(b-10) -150(b -10 +b) = 0

  5.5b^2 -5b -300b +1500 = 0 . . . . . . . . eliminate parentheses

  11b^2 -610b +3000 = 0 . . . . . . . . . . . . . multiply by 2

  (11b -60)(b -50) = 0 . . . . . . . . . . . . . . . . factor

The solutions to this equation are ...

  b = 60/11 = 5 5/11 . . . and . . . b = 50

Since b must be greater than 10, the first solution is extraneous, and the values of the variables are ...

  • b = 50
  • a = b-10 = 40
  • d = 5(a+b) = 5(90) = 450

The distance between A and B is 450 km.

_____

<u>Check</u>

<em>When the cars leave at the same time</em>, their speed of closure is the sum of their speeds. They will cover 450 km in ...

  (450 km)/(40 km/h +50 km/h) = 450/90 h = 5 h

__

<em>When car A leaves 4 1/2 hours early</em>, it covers a distance of ...

  (4.5 h)(40 km/h) = 180 km

before car B leaves. The distance remaining to be covered is ...

  450 km - 180 km = 270 km

When car B leaves, the two cars are closing at (40 +50) km/h = 90 km/h, so will cover that 270 km in ...

  (270 km)/(90 km/h) = 3 h

In that time, car B has traveled (3 h)(50 km/h) = 150 km away from city B, as required.

You might be interested in
A triangle has sides measuring 5 inches and 8 inches. If x represents the
lord [1]

Answer:

For me,the answer will be A.

im not sure

correct me if im wrong

love ya

6 0
2 years ago
Read 2 more answers
35 degrees - 45 degrees
love history [14]

Answer:

-10 degrees

Step-by-step explanation:

5 0
3 years ago
. A bar graph shows That Sports books received 9 votes. If the scale is to 20 by twos, Where should the bar end for the sports b
trasher [3.6K]
The bar should end halfway between 8 and 10.
3 0
3 years ago
Kelly walked 3 miles.Abby walk 3/4 of a mile how far did they walk in all
timofeeve [1]

Answer:

3 3/4

Step-by-step explanation:

Add the two numbers:

3 + 3/4 = 3 3/4

3 3/4 is the amount walked in all.

~

8 0
3 years ago
6 and 3 fourths plus 3 and 1 eighth<br> what is the answer?
AnnZ [28]

Answer:

9\frac{7}{8}

Step-by-step explanation:

6\frac{3}{4} + 3\frac{1}{8}, You have to make it so they have a common denominator

6\frac{6}{8}+ 3\frac{1}{8}

This would make the answer

9\frac{7}{8}

3 0
3 years ago
Other questions:
  • The name of the lesson is "Using Trigonometric Laws" The two non-parallel sides of an isosceles trapezoid are each 7 feet long.
    14·1 answer
  • You are picking up lumber at a lumber yard for a construction project. In addition to the ten (10) boards you already have, you
    11·2 answers
  • Find the expression below that is equivalent to 5^11/5^13
    12·2 answers
  • What is the slope of the line shown? <br> Please help
    9·1 answer
  • In circle F, the measures of angle ARE equals 120 and the measures of arc BD equals 50. What is the measure of angle C?
    15·1 answer
  • Which ordered pairs lie on the graph of the exponential function f(x)=−3^(x−1) +2 Select each correct answer.
    5·1 answer
  • The value of -4*2 is______
    12·2 answers
  • A gym membership in 2010 was $8,700. Now it is $6,400.
    7·1 answer
  • Calculate axis of symmetry and vertex for equation 4x squared + 8x = 32
    7·1 answer
  • Write an equation of the line passing through
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!