Respuesta :
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 =[tex]\frac{45}{60}=0.75 hours[/tex]
it takes 20 minutes to ride your bike down the mountain
20 minutes =[tex]\frac{20}{60}=0.33 hours[/tex]
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 .
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)
[tex]Speed=\frac{Distance}{time}[/tex]
[tex]X miles/hour=\frac{d}{0.75 hour}[/tex]
[tex]X miles=\frac{d}{0.75}[/tex]...(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
[tex](X+4)miles/hour=\frac{d}{0.33 hour}[/tex]
[tex](X+4) miles=\frac{d}{0.33}[/tex]
[tex]0.33X+1.32=d[/tex]...(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
