B. Solve
1. A bus covers a distance of 90 km at a uniform speed. Had the speed been 15
km/hour more it would have taken 30 minutes less for the journey. Find the
original speed of the bus.
2. If the difference between a number and its reciprocal is 24/5, find the number.
patulong po please, ayaw na po gumana ng utak ko. ubos na brain cells dahil sa ibang subject huehue.
1. A bus covers a distance of 90 km at a uniform speed. Had the speed been 15
km/hour more it would have taken 30 minutes less for the journey. Find the
original speed of the bus.
2. If the difference between a number and its reciprocal is 24/5, find the number.
patulong po please, ayaw na po gumana ng utak ko. ubos na brain cells dahil sa ibang subject huehue.
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Step-by-step explanation:
1. total distance = 90
Increased speed = x+15
90/x - 90/x+15=1/2
90(1/x - 1/x+15)=1/2
90(x+15-x/x^2+15x)=1/2
equation is:
x^2+15x-2700=0
x^2+60x-45x-2700=0
x(x+60)-45(x+60)=0
(x+60)(x-45)=0
x= -60, x=45
reject the negative value = -60
usual speed=45 km/ hr
2. Answer:
= 1/5
Step-by-step explanation:
Let x represent the number, then 1/x represents its reciprocal
The numeric relationship says; x - 2(1/x) = 24/5, solving
x^2 - 2 = (24/5)x
x^2 - (24/5)x - 2 = 0; use completing the square to solve; x^2 - (24/5)x = 2
Take 1/2 of the 24/5, the square of this will make a quadratic square
(1/2) *(24/5) = 12/5, therefore the 12/5 squared will be the third term of the quadratic square
x^2 - (24/5)x + 144/25 = 2 + 144/25 is where we want to get to, from the given,
Then (x - 12/5)^2 = 194/25
x - 12/5 = +- (194)^1/2/5; The only divisors of 194 are 1, 2, 97. and 194
There are no square factors of 194; 194^1/2 expresses the square root of 194
Thus x = +- (12/5 + (194)^1/2/5) or +-(12 + 194^1/2)/5
ANSWER IN NO. 1
PS. im not sure