A biker traveling at his usual speed can go from his house to work in 4 hours. When the weather is bad, he travels 6 miles per hour slower, and it takes him half an hour more. How far is his work from his house?

Answer 1

let the distance be x miles
let the normal speed by y mph

time at normal speed = x/y

but x/y = 4
x = 4y

time at slower speed = x/(y-6)

x/(y-6) = 4.5
4.5y - 27 = x
4.5y - 27 = 4y
.5y = 27
y = 54 , x = 4(54) = 216

He lives 216 miles from work.
normal speed is 54 mph.

check:
time to go to work = 216/54 = 4 hours
time go return = 216/48 = 4.5 , which is 1/2 hour more.

I assume that is a motorbike. Still, 216 miles to go to work??
Silly question.

Answer 2

let the distance be x miles
let the normal speed by y mph

time at normal speed = x/y

but x/y = 4
x = 4y

time at slower speed = x/(y-6)

x/(y-6) = 4.5
4.5y - 27 = x
4.5y - 27 = 4y
.5y = 27
y = 54 , x = 4(54) = 216

He lives 216 miles from work.
normal speed is 54 mph.

check:
time to go to work = 216/54 = 4 hours
time go return = 216/48 = 4.5 , which is 1/2 hour more.

I assume that is a motorbike. Still, 216 miles to go to work??
Silly question.

Answer 3

let the distance be x miles
let the normal speed by y mph

time at normal speed = x/y

but x/y = 4
x = 4y

time at slower speed = x/(y-6)

x/(y-6) = 4.5
4.5y - 27 = x
4.5y - 27 = 4y
.5y = 27
y = 54 , x = 4(54) = 216

He lives 216 miles from work.
normal speed is 54 mph.

check:
time to go to work = 216/54 = 4 hours
time go return = 216/48 = 4.5 , which is 1/2 hour more.

I assume that is a motorbike. Still, 216 miles to go to work??
Silly question.