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Monica [59]
3 years ago
5

A train leaves San Diego at 1:00 pm. A second train leaves the same city in the same direction at 3:00 pm. The second train trav

els 30 mph faster then the first. If the second train overtakes the first at 6:00 pm, what is the the speed of each of the two trains?
Mathematics
1 answer:
Soloha48 [4]3 years ago
7 0

Answer:

The speed of the first train is 45 mph and the speed of the second train is 75 mph

Step-by-step explanation:

Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).

The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles

The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles

Since the second train overtakes the first at 6:00 pm, hence:

3x + 90 = 5x

2x = 90

x = 45

Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).

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Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.
yan [13]

Answer:

a. Of all the students, \frac{1}{5} are girls with blond hair.

b. Of all the students, \frac{1}{5} are boys without brown hair.

Step-by-step explanation:

a. You know that \frac{3}{5} of the students are girls (This means that \frac{2}{5} of the studes are boys) and \frac{1}{3} of these girls have blond hair.

Then, \frac{1}{3} of \frac{3}{5} is:

(\frac{3}{5})(\frac{1}{3})=\frac{1}{5}

Therefore, of all the students, \frac{1}{5} are girls with blond hair.

b. You know that \frac{1}{2} of the boys have brown hair.

Then, \frac{1}{2} of \frac{2}{5} is:

(\frac{2}{5})(\frac{1}{2})=\frac{1}{5}

Of all the students, \frac{1}{5} are boys without brown hair.

8 0
3 years ago
The following are the distances (in miles) to the nearest airport for 12 families. 6, 7, 8, 8, 16, 19, 23, 24, 26, 27, 34, 35 No
AveGali [126]

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

  • Minimum: 6
  • Lower quartile: 8
  • Median: 21.
  • Upper quartile: 27
  • Maximum: 35
  • Interquartile range: 19

<h3>What are the median and the quartiles of a data-set?</h3>

  • The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
  • The first quartile is the median of the first half of the data-set.
  • The third quartile is the median of the second half of the data-set.
  • The interquartile range is the difference of the third quartile and the first quartile.

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The first quartile is the median of 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

More can be learned about the five-number summary and the interquartile range at brainly.com/question/3876456

#SPJ1

4 0
2 years ago
A home has a room with length 22 feet and width 25 ft.
Elena L [17]

Answer:

O length = 11 inches width = 12.5 inches

Step-by-step explanation:

8 0
3 years ago
If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test neg
k0ka [10]

Answer:

0.0098

Step-by-step explanation:

Probability of being pregnant:100/1000

=1/10.

98% chance:=98/100 ×1/10

=98/1000

Therefore the probability that she really is pregnant is: 0.098

3 0
3 years ago
80% is what fraction of the whole quantity?
USPshnik [31]
The answer is 80/100
8 0
3 years ago
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