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

Answer 1

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

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=(Distance)/(time)`

`X miles/hour=(d)/(0.75 hour)`

`X miles=(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=(d)/(0.33 hour)`

`(X+4) miles=(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

Answer 2

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 =
`(45)/(60)=0.75 hours`

it takes 20 minutes to ride your bike down the mountain

20 minutes =
`(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 .