Rsm question need 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?

Work Shown:

d = distance from work to his house

x = speed when weather is good

y = speed when weather is bad

y = x-6 since he travels 6 mph slower

On a good weather day, he travels for 4 hours and goes at x mph

distance = rate*time

d = r*t

d = x*4

d = 4x

On a bad weather day, he travels 4.5 hours (half hour more than 4 hrs) and goes at y = x-6 mph

d = r*t

d = y*4.5

d = 4.5y

d = 4.5(x-6) replace y with x-6

d = 4.5x-27 distribute

The values of d for both equations are the same, as the biker is traveling the same distance. So we can equate the two right hand sides (RHS) and solve for x.

4.5x-27 = 4x

4.5x-4x = 27

0.5x = 27

x = 27/0.5

x = 54

The biker's speed on a good weather day is 54 mph.

A bad weather day's speed would be y = x-6 = 54 - 6 = 48 mph.

Now compute the value of d

d = 4x

d = 4*54

d = 216

The biker travels 216 miles on a good weather day

or,

d = 4.5*y

d = 4.5*48

d = 216

the biker travels that same distance on a bad weather day.