Marlene rides her bicycle to her friend jon's house and returns home by the same route. marlene rides her bike at constant speeds of 6 mph on level ground, 4 mph when going uphill and 12 mph when going downhill. if her total time riding was 2 hours, how far is it to jon's house?

Jon's house is 6 miles further away from Marlene's house.

Given that:

Speed on level ground is 6 mph

Speed on uphills is 4 mph

Speed on downhills is 12 mph

Let there are x miles level ground and y miles hills(either up or low, which while returning to home will serve as low or up respectively) in the route, then the whole route's length is x + y miles.

Since time taken = distance/speed , thus we have:

Since x + y denotes the length of the whole route(one sided), thus, Jon's house is 6 miles further away from Marlene's house.

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x = level ground

y = hills

x/6 +y/4 +y/12 + x/6 = 2 hours

 multiply everything by 12 to get rid of the denominators:

 equation becomes 2x +3y +y +2x = 24

 combine like terms:

4x +4y = 24

 divide everything by 4

 f +h = 6 miles to Jon's house

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places