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zaharov [31]
3 years ago
10

Mr. Monasterio ran to the store for burritos at 4 miles per hour. On the way back, he increased his speed to 6 miles per hour. I

f the whole trip took 2 hours, how long was the trip to the store? Put your answer in decimal form.
Mathematics
1 answer:
sveticcg [70]3 years ago
7 0

Answer:

It took 1.2 hours to get to the store

Step-by-step explanation:

Let the time taken to reach the store be t₁

Let the time taken to come back be t₂

Let the speed to and from store = s₁ and s₂ respectively

let the distance to the store = d

To the store:

speed = \frac{distance}{time} \\s = \frac{d}{t_1} \\t_1 = \frac{d}{s_1}\\t_1 =\frac{d}{4} - - - - - (1)

Back from the store:

s_2 = \frac{d}{t_2} \\t_2 = \frac{d}{s_2}\\where:\\s_2 = 6\ miles\ per\ hour\\t_2 = \frac{d}{6} - - - - - - (2)

We are told that total time (t₁ + t₂) = 2 hours

t₁ + t₂ = eqn (1) + eqn (2)

\frac{d}{4} + \frac{d}{6} = 2\\Multiplying\ through\ by\ 12:\\3d\ +\ 2d\ =\ 24\\5d = 24\\d = \frac{24}{5} \\d = 4.8\ miles

∴ length of trip to the store = t₁

from eqn (1)

t_1 = \frac{d}{4} \\t_1 = \frac{4.8}{4} \\t_1 = 1.2\ hours

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In how many ways can 100 identical chairs be distributed to five different classrooms if the two largest rooms together receive
Eva8 [605]

Answer:

There are 67626 ways of distributing the chairs.

Step-by-step explanation:

This is a combinatorial problem of balls and sticks. In order to represent a way of distributing n identical chairs to k classrooms we can align n balls and k-1 sticks. The first classroom will receive as many chairs as the amount of balls before the first stick. The second one will receive as many chairs as the amount of balls between the first and the second stick, the third classroom will receive the amount between the second and third stick and so on (if 2 sticks are one next to the other, then the respective classroom receives 0 chairs).

The total amount of ways to distribute n chairs to k classrooms as a result, is the total amount of ways to put k-1 sticks and n balls in a line. This can be represented by picking k-1 places for the sticks from n+k-1 places available; thus the cardinality will be the combinatorial number of n+k-1 with k-1, {n+k-1 \choose k-1} .

For the 2 largest classrooms we distribute n = 50 chairs. Here k = 2, thus the total amount of ways to distribute them is {50+2-1 \choose 2-1} = 51 .

For the 3 remaining classrooms (k=3) we need to distribute the remaining 50 chairs, here we have {50+3-1 \choose 3-1} = {52 \choose 2} = 1326 ways of making the distribution.

As a result, the total amount of possibilities for the chairs to be distributed is 51*1326 = 67626.

7 0
3 years ago
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Step-by-step explanation:

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