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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 =
it takes 20 minutes to ride your bike down the mountain
20 minutes =
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 .