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?
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.
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.
To find the distance from his house to work, we need to first determine the biker's usual speed.
Let's assume the biker's usual speed is "x" miles per hour.
According to the problem, when the weather is bad, the biker travels 6 miles per hour slower. Therefore, his speed during bad weather is (x - 6) miles per hour.
When the weather is good, he takes 4 hours to travel from his house to work. We can use the formula "Distance = Speed × Time" to calculate the distance: Distance_good = (x miles/hour) × (4 hours).
When the weather is bad, he takes 0.5 hours more than his usual time. So, the time taken during bad weather is 4 + 0.5 = 4.5 hours. Again, we can use the same formula to calculate the distance: Distance_bad = (x - 6 miles/hour) × (4.5 hours).
Since the distance from his house to work remains the same, we can set the two distances equal to each other and solve for x.
Distance_good = Distance_bad
(x miles/hour) × (4 hours) = (x - 6 miles/hour) × (4.5 hours)
Simplifying the equation:
4x = 4.5x - 27
Rearranging and solving for x:
0.5x = 27
x = 27 / 0.5
x = 54
The biker's usual speed is 54 miles per hour.
Now, to find the distance from his house to work, we can substitute this speed back into the formula:
Distance_good = (54 miles/hour) × (4 hours)
Distance_good = 216 miles
Therefore, his work is 216 miles away from his house.
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.