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3 years ago

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On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40

minutes longer to climb up than run down, what is the total length of Ted's hike?

2 answers:

Hitman42 [59]3 years ago

4 0

So the other guy has the right work but at the end he messed up. The real answer is 10 miles.

telo118 [61]3 years ago

3 0

It takes 40 minutes more going up or 40/60 = 0.67 hours more.

Let us say that:

t = the time required for him running down

t + 0.67 = time required for him running up

Since the distance of running up and down must be equal therefore:

(3 miles / hr) * (t + 0.67) = (5 miles / h) * t

3 t + 2.01 = 5 t

2 t = 2.01

t = 1.005 hr

So the total length of the hike is:

length = 2 * (5 miles / hr) * (1.005 hr)

<span>length = 10.05 miles</span>

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Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

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The exact answer is going to be found using the compound interest formula.

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

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The interest is compounded anually, so $n = 1$

$A = P(1 + \frac{r}{n})^{nt}$

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

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Answer:

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Step-by-step explanation:

we are given a quadratic function

$\displaystyle f(x) = - 5 {x}^{2} + 30x - 200$

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$\displaystyle x _{ \rm min} = \frac{ - b}{2a}$

the given function is in the standard form i.e

$\displaystyle f(x) = a {x}^{2} + bx + c$

so we acquire:

b=30
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thus substitute:

$\displaystyle x _{ \rm min} = \frac{ - 30}{2. - 5}$

simplify multiplication:

$\displaystyle x _{ \rm min} = \frac{ - 30}{ - 10}$

simply division:

$\displaystyle x _{ \rm min} = 3$

plug in the value of minimum x to the given function:

$\displaystyle f (3)= - 5 {(3)}^{2} + 30.3 - 200$

simplify square:

$\displaystyle f (3)= - 5 {(9)}^{} + 30.3 - 200$

simplify multiplication:

$\displaystyle f (3)= - 45 + 90- 200$

simplify:

$\displaystyle f (3)= - 155$

hence,

the minimum value of the function is -155

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