you ride your bike X miles per hour up a mountain for 45 minutes on the way down the mountain you ride your bike for 4 miles per hour faster

Question

you ride your bike X miles per hour up a mountain for 45 minutes on the way down the mountain you ride your bike for 4 miles per hour fasterit takes 20 minutes to ride your bike down the mountain how far did you ride your bike in total

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Answers ( No )

    0
    2021-10-11T02:40:40+00:00

    Answer:

    The total distance covered during riding up and down the mountain is 4.714 miles.

    Step-by-step explanation:

    Speed of the bike while riding  up mountain = X mile/hour

    Distance covered be d.

    Time taken to cover d distance = 45 minutes = 0.75 hour

    (1 hour = 60 min)

    Speed=\frac{Distance}{time}

    X miles/hour=\frac{d}{0.75 hour}

    X miles=\frac{d}{0.75}…(1)

    Speed of the bike while riding  down mountain = (X+4) mile/hour

    Distance covered while moving down the mountain = d.

    Time taken to cover d distance = 20 minutes = 0.33 hour

    (X+4)miles/hour=\frac{d}{0.33 hour}

    (X+4) miles=\frac{d}{0.33}

    0.33X+1.32=d…(2)

    O solving (1) and (2):

    we get, d = 2.357 miles

    X = 3.143 miles/hour

    Total distance covered by us = d + d= 2.357 miles+ 2.357 miles = 4.714 miles

    0
    2021-10-11T02:41:28+00:00

    you ride your bike X miles per hour up a mountain for 45 minutes on the way

    We convert minutes into hour because speed is in miles per hour

    To convert minutes into hour we divide by 60

    45 minutes =\frac{45}{60}=0.75 hours

    it takes 20 minutes to ride your bike down the mountain

    20 minutes =\frac{20}{60}=0.33 hours

    you ride your bike X miles per hour up a mountain

    Distance = speed * time taken

    distance covered while riding bike up a mountain is

    D = x *0.75

    on the way down the mountain you ride your bike for 4 miles per hour faster

    So time taken is x + 4

    distance covered while riding bike up a mountain is

    D =  (x+4) * 0.33

    Distance covered by climbing up and down the mountain are same

    so we make the distance equation equal

    x *0.75=  (x+4) * 0.33

    0.75x = 0.33x + 1.32

    Subtract 0.33 from both sides

    0.42x = 1.32

    Divide both sides by 0.42

    x = 3.1429  miles per hour

    Distance covered up D = 0.75* x = 0.75 * 3.1429 = 2.357175

    Distance covered down D = (3.1429 +4) * 0.33 =  2.357157

    Total distance covered = 2.357175 + 2.357175 = 4.71435

    you ride your bike in total of 4.71 miles approximately .

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