I have a word problem I cannot solve. I need the formula and a one-time answer for my homework?

Question

During rush hour, Bill can drive 15 miles using the side roads in the same time that it takes to travel 10 miles on the freeway. If Bill's rate on the side roads is 8 mi/h faster than his rate on the freeway, find his rate on the side roads.

Answer 1

Let the time it takes Bill to drive 15 miles on the side roads be x. This is also the time it takes him to drive 10 miles on the freeway.

We usually express the rate of travel as miles per hour. In this case, its miles per x hours.

You also know that the rate on the side roads is 8miles per hour faster than the freeway.

This is expressed as rate on side rds = rate on fwy + 8mph
15/x = 10/x + 8/1

Mult both sides by x
15 = 10 + 8x

5 = 8x
5/8 = x where x is the amount of time in hours Bill traveled

His speed on the side roads is 15/x = 15/(5/8) = (8*15)/5 = 8*3 = 24mph

Answer 2

on the side way, the velocity of Bill is v+8
you can write x=v*t where v=velocity on freeway, t time

so 15 = (v+8) *t and 10=vt

15 = vt + 8t = 10+8t

5=8t t=5/8 v =80/5 =16 km/h

and on the side roads 16+8 = 24 km/h

Answer 3

S- space
v- velocity
t- time

S1= 10mi
S2= 15mi

t1=t2
v2=v1+8

S=v X t

t=S/v

S1/v1=S2/v1+8

15 X v1= 10 X v1 + 80

5 X v1= 80

v1= 16

v2= 24 mi/h