Linear Equation In one Unknown

2012-08-13 11:20 pm
我只係想要算式同埋簡易淺白嘅解釋,,,Step同Ans唔洗啦:)

1. The sum of two consecutive integers is 83. Find these two integers.

2. Stephanie and Dennis go hiking together. They go uphill at a speed of 3m/h and downhill at a speed of 4m/h. If the lengths of the uphill and the downhill paths are the same, and Stephanie and Dennis spend a total of 4.2hrs in completing their journey, find the total length of the journey.

3. In a two-digit n umber, the units digit is greater than the tens digit by 3. If the tens digit and the units digit of the number are interchanged,the sum of the number obtained and the original number is 121.Find the two numbers.
更新1:

Re 胡雪: 我想問Q2嘅0.5係點黎:)?

回答 (1)

2012-08-14 12:04 am
✔ 最佳答案
1.
Let n be the smaller integer.
They are two consecutive (連續的) integers.
Then the larger integer = n + 1

Sum of the two numbers = 83 :
n + (n + 1) = 83
2n = 82
n = 41

The two integers are 41 and 42.


*****
2.
Let d m be the total length of the journey.
Then, Distance for uphill = Distance for downhill = 0.5d m

Time = Distance/Speed
Time for uphill + Time for downhill = 4.2 h

(Distance for uphill)/(Speed for uphill) + (Distance for downhill)/(Speed for downhill)= 4.2 h :
(0.5d/4) + (0.5d/3) = 4.2
12[(0.5d/4) + (0.5d/3)] = 12(4.2)
1.5d + 2d = 50.4
d = 14.4

The total length of the journey is 14.4 m.
(It will be more realistic if the unit of length is km instead of m.)


*****
3.
Let t the tens digit.
The unit digit is greater than the tens digit by 3.
Then, the units digit = t + 3

The value of a two-digit number = (10 x tens digit) + units digit
Hence, the original number = 10t + (t + 3)
and the new number obtained by interchanging the two digits = 10(t + 3) + t

Sum of the original number and the new number obtained = 121 :
[10t + (t + 3)] + [10(t + 3) + t] = 121
22t = 88
t = 4
t + 3 = 7

The original number is 47. The new number obtained is 74.

2012-08-14 01:55:06 補充:
2.
Length of uphill part = Length of downhill part

But (Length of uphill part) + (Length of downhill part) = d m
Then, Length of uphill part = Length of downhill part = 0.5d m
參考: 胡雪, 胡雪


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